Abishai in Fausset's Bible Dictionary

("father of gifts".) Nephew of David by his sister Zeruiah; brother of Joab and Asahel. Joab was more of the experienced general, Abishai the devoted champion for David. Thus, when David proposed to Ahimelech the Hittite and Abishai the perilous visit to Saul's camp, Abishai instantly volunteered, reckless of personal danger. His impulsive nature needed occasional checking, in his zeal for David. We find the consistency of character maintained throughout the history; the same spirit prompting the request at Hachilah," Let me smite Saul" (1 Samuel 26:8), as subsequently at Bahurim, when Shimei cursed David, prompted his exclamation "Why should this dead dog curse my Lord the king? let me take off his head" (2 Samuel 16:9). He commanded one third of David's army at the battle with Absalom (2 Samuel 18), and rescued David when waxing faint and in imminent peril from the giant Ishbi-benob (2 Samuel 21:15-17). In the same war probably he, as chief of the three "mighties," chivalrously broke through the Philistine host to procure water for David from the well of his native Bethlehem (2 Samuel 23:14-17). Once he withstood 300 and slew them with his spear. In 2 Samuel 8:13 the victory over the 15,000 Edomites or Syrians in the Valley of Salt is ascribed to David; in 1 Chronicles 18:12, to Abishai. Probably the commander in chief was David, but the victory actually gained by Abishai.

Link: https://bible-history.com/faussets/A/Abishai/