Green’s Dictionary of Slang

a difficult, surprising, embarrassing or pointed question.

1849		Thackeray Pendennis I 252: Sir Francis turned to the guest on his left, and whispered. ‘That’s what I call a sticker for Wagg.’.
1890–1904		Farmer & Henley Sl. and Its Analogues.
1905		‘Central Connecticut Word-List’ in DN III:i 21: sticker, n. A difficult question or task. ‘That’s a sticker,’ i.e. hard to answer.
1950		S. Murphy Stone Mad (1966) 79: The Confession on Saturday is a bit of a sticker for me – I have to dress up and go down town and have a few pints before I can face it.