Green’s Dictionary of Slang

to pay for (someone else).

1936		J. Curtis Gilt Kid 68: ‘Have you got a chat of your own?’ ‘I got a place of my own, but the old steamer’s pestering.’.
1937		J. Curtis There Ain’t No Justice 205: Bloody sight more than you earned before. Bloody sight more than I could have afforded to pester for straight fights.
1937		J. Curtis You’re in the Racket, Too 58: He must have got some dough if he’ll pester that and drop you a bit and all. [Ibid.] 64: Slip us the dough before we go out. I don’t want any one to see you pestering for me. They’d make out I was a ponce or something.
1950		P. Hoskins No Hiding Place! 191/2: Pester Up. Pay up.