I urge (3870) (parakaleo [word study] from para = side of, alongside, beside + kaleo [word study] = call) means literally to call one alongside, to call someone to oneself, to call for, to summon. Parakaleo can include the idea of giving help or aid but the primary sense in the NT is to urge someone to take some action, especially some ethical course of action. Sometimes the word means convey the idea of comfort, sometimes of exhortation but always at the root there is the idea of enabling a person to meet some difficult situation with confidence and with gallantry. See the following discussion for elaboration on the nuances of this great Greek verb.

Urge (Latin urgere = to press, push) which means to press, to push,  to drive, to impel,  to apply force to, to press the mind or will, to press by motives, arguments, persuasion or importunity.

Kent Hughes illustrates the root idea of parakaleo "to come alongside and encourage" with the following example

I see this exemplified every time my church has a roller skating party, and the parents put their little ones on skates for the first time. Mom and Dad skate with their child, holding on to his or her hands, sometimes with the child’s feet on the ground and sometimes in the air. But all the time the parents are alongside encouraging....[exhortation] is a wonderful gift, and we are to place it at Christ’s feet and be willing to be worn out in its use.

BEAR WITH THIS WORD OF EXHORTATION: anechesthe (2PPMM) tou logou tes parakleseos:

THE PURPOSE
FOR THIS EPISTLE:
EXHORTATION

Bear (430) (anechomai [word study] from aná = in, up + echomai, the middle voice of echo = to have, to hold)  means literally to hold one’s self erect, upright and firm against a person or thing. Thus anechomai means to put up with, to bear with (equanimity or evenness of mind especially under stress), to tolerate, to forbear, to be patient with.

The present imperative is a command to the readers to keep on receiving, keep on listening. The readers are to keep on running the race and not be disqualified! (Cp Heb10:35-note, 1Co9:27)

Preach (aorist imperative - Do this now! Don't delay! It sometimes even conveys a sense of urgency - same tense and voice for all the following verbs) the word; be ready in season and out of season; reprove, rebuke, exhort, with great patience and instruction. For the time will come when they will not endure (anechomai) sound doctrine; but wanting to have their ears tickled, they will accumulate for themselves teachers in accordance to their own desires (2Ti 4:2-note, 2Ti 4:3-note)

FOR I HAVE WRITTEN TO YOU BRIEFLY: kai gar dia bracheon epesteila (1SAAI) humin:

Vine adds that

Though the epistle is itself comparatively long, it is short considering the supreme importance of the subject. The writer has indicated, for instance, in He 5:11-note that he had more to say on the subject he was handling. (Vine, W. Collected writings of W. E. Vine. Nashville: Thomas Nelson or Logos)

Steven Cole writes that...

You should obey godly leaders by obeying their exhortations from God’s Word. In He 13:22, the author says, “But I urge [lit., exhort“] you, brethren, bear with this word of exhortation, for I have written to you briefly.” Some may think that a 13-chapter letter is not on the brief side, but it can be read aloud in 48 minutes. Given the weighty subject matter, that’s not too bad! Three times the author has indicated that he could say much more, but he restrained himself (He 5:11-note; He 9:5-note; He 11:32-note). (I can identify with that problem!) The word “exhortation” is used of a sermon (Acts 13:15). So even if the sermon runs almost an hour, you should bear with it and seek to obey it!

The word “bear with” is translated “endure” in 2Ti 4:3-note. After charging Timothy to “preach the Word,” which includes “re-prove, rebuke, exhort” (2Ti 4:2-note), Paul adds,

“For the time will come when they will not endure sound doctrine; but wanting to have their ears tickled, they will accumulate for themselves teachers in accordance to their own desires.”

The reason you must bear with or endure sound doctrine is that it often confronts how you think or live, showing you God’s different way (“reproof,” 2Ti 3:16-note; 2Ti 4:2-note). Because they want to please people, many pastors shrink from declaring “the whole purpose of God” (Acts 20:27). They think, “the doctrine of election is too controversial,” so they don’t preach on it, even though it’s in the Bible for our spiritual profit. Or they would dodge our text, which talks about obedience and submission to church leaders, because it might upset too many people. They dodge talking about male leadership in the church and home, because that upsets the feminists. Pretty soon, the Bible becomes a tame book of platitudes that allow everyone to live as they please!

Of course leaders must exhort with patience and gentleness. We must allow people time to wrestle with difficult truth as they grow in Christ. Spiritual maturity, like physical and emotional maturity, takes time. But, on the listening end, if you want to grow in Christ, you must bear with the exhortations of your spiritual leaders. Don’t shrug off things you don’t agree with. Go back to Scripture and see if these things are true. If they are, submit to them as the Word of God, not the word of men (1Th 2:13-note).

Fabarez did some research and found

“that most people do not prepare in any significant way for church....In an average church, fewer than half of the worshipers pray for their encounter with the sermon. Less than a third pray for their or his preparation. Even when the passage is clearly announced the previous week, only one in five people will take the time to read it before they come to church” (Michael Fabarez, Preaching that Changes Lives [Thomas Nelson Publishers], p. 153).

If you want to “bear with” the word of exhortation that I bring each week, I would encourage you to pray for your own heart to be receptive to God’s truth. Pray for me as I prepare the message and preach it, that I would be faithful to the text of Scripture. And, spend some time during the week going over the passage itself, meditating on how it applies to your heart.

The effectiveness of my preaching does not just depend on how well I preach, but also on how well you listen.

Even Jesus, the greatest preacher ever, exhorted His audience, “Take care how you listen” (Luke 8:18). Your first duty is to obey godly church leaders, and that primarily means obeying the Word of God that they preach. (Hebrews 13:17-19, 22-25 Your Duties Toward Church Leaders)

Guzik comments that...

Greet (782) (aspazomai from a  + spao = draw out as a sword, pull, breathe) (aorist imperative = command to carry this out effectively. Be sure to greet them!) means to enfold in arms, welcome, embrace. It is spoken of those who meet or separate. This is often one final expression in Paul's epistles (another reason some think he may be the author of Hebrews). Aspazomai is constantly used in the papyri for conveying the greetings at the end of a letter.

Aspazomai - 59x in 47v - Matt 5:47; 10:12; Mark 9:15; 15:18; Luke 1:40; 10:4; Acts 18:22; 20:1; 21:7, 19; 25:13; Rom 16:3, 5ff, 21ff; 1 Cor 16:19f; 2 Cor 13:12; Phil 4:21f; Col 4:10, 12, 14f; 1 Thess 5:26; 2 Tim 4:19, 21; Titus 3:15; Phlm 1:23; Heb 11:13; 13:24; 1 Pet 5:13f; 2 John 1:13; 3 John 1:15. NAS = acclaim(1), give...your greeting(1), greet(41), greeted(3), greeting(1), greets(5), paid their respects to(1), sends...greetings(4), taken...leave(1), welcomed(1).

Leaders (2233) (hegeomai [word study] from ago = to lead, carry, bring) has two basic meanings in the NT. One is to lead as one would do in a supervisory capacity as when describing men in any leading position - ruler, leader, governor (Ac 7:10) and stands opposite of a diakonos or servant in (Lk 22:26). In the apocryphal writings hegeomai was used of military commanders. It was also used to describe leaders of religious bodies, both pagan and Christian (Heb 13:7, 17, 24, "leading men" in Acts 15:22, "chief speaker" in Acts 14:12).

What a great way to end our "race of grace"! To God be all the glory. Amen.

Guzik notes that grace marks a...
 

fitting end for a book that documents the passing of the Old Covenant and the institution of the New Covenant. Grace be with you all indeed, under what God has given through the superior Savior, Jesus Christ! Amen!

Vine adds that

grace here is the divine favor manifested in blessing at all times and in all experiences. (Vine, W. Collected writings of W. E. Vine. Nashville: Thomas Nelson or Logos)

Grace (5485) (charis [word study] from from chairo = to rejoice. English = charity. Beggars need "charity" even as sinners need grace, for we are all spiritual paupers outside of Christ, but "God gives where he finds empty hands"-Augustine [cp Mt 5:3-note]) is a word which defies a simple definition but at its core conveys the sense of favor while the specific nuances of charis depend on the context in which it is used.

Someone has written that the word grace is probably the greatest word in the Scriptures, even greater even than “love,” because grace is love in action, and therefore includes it. It is hardly too much to say that God has in no word uttered Himself and all that was in His heart more distinctly than in this word grace (charis)!

The English word grace is from the Latin gratia meaning favor, charm or thanks. Gratia in turn is derived from gratus meaning free, ready, quick, willing, prompt. Webster defines grace as the...