Green’s Dictionary of Slang

strap v.2

[strap n.5 ]

1. to give credit.

[UK]C.C. Robinson Dial. Leeds 423: ‘Yuh mun strap muh this missis wal Seterder neet.’ [...] ‘D’ yuh strap here master?’ .
[UK]Evesham Journal 26 Sept. n.p.: Witness said she had not got a sixpence, and prisoner offered to ‘strap’ it with her [EDD].
[Aus]Sydney Sportsman (Surry Hills, NSW) 8 June 3/3: ‘Do you know the accused?’ ‘Well (doubtingly) that depends. When he lias the money to pay for the drinks, I do; but when he wants me to strap it up - I don’t’.
[UK](con. 1920s) J. White ‘Campbell Bunk’ in History Workshop 21: The provision dealers gave credit - ‘going on the strap’ or ‘strapping it’ - it was called.

2. (Aus.) to obtain a loan, to borrow.

[Aus]Sun. Mail (Brisbane) 13 Nov. 20/8: ‘So-and-so strapped me for a shwe to-day. He was in a yike up north and copped a blue. Had to do a tommy-off and he is down here in smoke.’ Translated, someone had borrowed a florin from the speaker. He had got into trouble in the north and with a warrant issued for his arrest had escaped by boat and had gone into hiding.

In phrases

strap up (v.)

(Aus., also strap it) to obtain on credit; to offer credit.

[Aus]Sun. Times (Perth) 7 Oct. 1/1: A boss-cop swills as many snifters as he can hold, and straps it for eternity.
[Aus]Bulletin (Sydney) 10 Dec. 38/3: The premises were then let as a boot hospital. [...] The derelicts and no-accounts gravitated to his place as though by a law of Nature. [...] They sat upon their heels in perspiring rows, took ‘squints’ at his newspaper, and criticised bitterly the actions of persons in authority. Sometimes they bought a penny pair of laces from Ryan and ‘strapped’ the purchase up.
[Aus]Baker Popular Dict. Aus. Sl.
[Aus]N. Pulliam I Travelled a Lonely Land (1957) 240/1: strap up – buy on credit.
[Aus] ‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xl 4/5: strap up: To obtain credit.