Green’s Dictionary of Slang

1. (US black) to boast and then to retreat from one’s claims.

1969		T. Kochman ‘“Rapping” in the Black Ghetto’Trans-action Feb. 31/1: ‘Gripping’ is of fairly recent vintage, used by black high school students in Chicago to refer to the talk and facial expression that accompanies a partial loss of face or self-possession, or showing of fear.
1971		H.E. Roberts Third Ear n.p.: grip v. to beg one’s way out of a situation by self-depreciation; e.g. Dig him trying to grip to that broad.

2. to recount boastful stories.

1971

(con. WWII) B. Aldiss Soldier Erect 93: We invented lecherous fantasies and ‘gripped’ at each other. [Ibid.] 96: When Corporal Warren started to say, ‘When I was stationed in Malta’, several voices cried ‘Grip on!’.