Green’s Dictionary of Slang

(UK Und.) cat burglary; thus at the climb, climbing, working as a cat burglar.

1930		(con. 1910s) D. Mackenzie Hell’s Kitchen 124: When any sort of climb is indulged in it is referred to as ‘at the climb’ [...] ‘At the climb’ is usually done during the evening, frequently when the occupants of the house are at dinner. [Ibid.] 125: ‘Climbing’ is indulged in by high-class crooks.
1935		G. Ingram Cockney Cavalcade 256: Do you know anything of that climbing job up West the other night?
1935		Thieves Slang ms list from District Police Training Centre, Ryton-on-Dunsmore, Warwicks 1: At the climb: Cat burglar.
1949		Monteleone Criminal Sl. (rev. edn).
1961		(con. 1920s) J. Sparks Burglar to the Nobility 19: George McCraig, a cat-burglar very well respected in the business [...] At the climb, there was no doubt, Georgie McCraig was the Royal Scot.