Green’s Dictionary of Slang

to have sexual intercourse with; to seduce.

1971		W. Amidon Charge..! 67: He [...] found it a drag to have a chick belching in his ear while he was strumping her.
1986		F. Taylor Auf Wiedersehen Pet Two 124: I’d have had second thoughts about strumpin’ his daughter. [Ibid.] 251: I tried to strump that dark-haired one in the lift.