John Gill Commentary 2 Samuel 18:19

"Then said Ahimaaz the son of Zadok, Let me now run, and bear the king tidings, how that Jehovah hath avenged him of his enemies." — 2 Samuel 18:19 (ASV)

Then said Ahimaaz the son of Zadok
To Joab; for it seems he stayed with the army when he with Jonathan brought the message from Hushai to David:

let me now run, and bear the king tidings how that the Lord has
avenged him on his enemies ;
which he thought would be very acceptable to hear of as soon as possible; and to be a messenger with tidings of a victory, as it was honourable, so likewise profitable then as now.

Though perhaps Ahimaaz might have no respect to the reward, as indeed none could be expected, since the death of Absalom would be so disagreeable to the king; but was desirous of it, that the king might be acquainted with the event of the battle as soon as might be.