Green’s Dictionary of Slang

(UK/US Und.) a cat burglar.

1891		Emporia Dly Repub. (KS) 28 Apr. 3/2: A thief who robs houses in the early evening is called [...] ‘climber’.
1900		Flynt & Walton Powers That Prey 64: I say that we hunt up a good sneak an’ climber (sneak-thief and burglar).
1989		J. Morton Lowspeak 39: Climber – a burglar who literally climbs up the outside of buildings, particularly hotels. There is now said to be only one working in London.