Adam Clarke on 2 Samuel 19:11

Speak unto the elders of Judah - David was afraid to fall out with this tribe: they were in possession of Jerusalem, and this was a city of great importance to him. They had joined Absalom in his rebellion; and doubtless were now ashamed of their conduct. David appears to take no notice of their infidelity, but rather to place confidence in them, that their confidence in him might be naturally excited: and, to oblige them yet farther, purposes to make Amasa captain of the host in the place of Joab.