Green’s Dictionary of Slang

1. to hang.

1824

Egan Recollections of J. Thurtell 40: I understand that when you round (hang) people here, you put them in a tumbler (cart) and send them out of the world.

2. to elicit information from someone by trickery.

1854

A.E. Baker Northampt. Gloss. n.p.: 1. "To round her." To endeavour to obtain information indirectly or by artifice. ‘I’ll round her, and get the secret out before I’ve done with her ’.

3. (Aus./UK Und.) to inform; to confess, to tell the truth.

1895		C. Crowe Aus. Sl. Dict. 68: Rounding, informing; from round, to tell tales.
1901		J. Caminada Twenty-Five Years of Detective Life II 354: It looked as if the son had carried it home and the old lady prevailed upon him to ‘round.’.

4. to obtain information about someone by questioning a third party .

1904		‘Number 1500’ Life In Sing Sing 251: Rounding. Betraying.
1929		J.B. Booth London Town 310: If he ‘rounded’ about Cherry and pleaded guilty to his present trouble [...] he should get off with a light sentence?
1949		Monteleone Criminal Sl. (rev. edn) 197: rounding Betraying.