Green’s Dictionary of Slang

1. in card games, securing the good cards behind the head or in one’s hat.

1803

Sporting Mag. Feb. XXI 326/2: Garreting – Is so called from the practice of securing the good cards at any time behind the head, under the hat.

2. (UK Und.) robbing a house by entering through an upper or garret window.

1859		Matsell Vocabulum.
1862		Newcastle Jrnl 30 Dec. 2/6: Perhaps your house is regularly broken into; [...] ‘Jumping a crib,’ is entrance by a window; ‘breaking a crib,’ forcing a backdoor; ‘grating a crib,’ through cellar gratings; ‘garreting a crib,’ through the roof or by an attic window.
1865		Leaves from Diary of Celebrated Burglar 63/2: Eyes had been doing some tall ‘garreting’ (not garroting) that season and was pretty flush of ‘sugar’.