Green’s Dictionary of Slang

under wraps adv.

restrainedly.

1907		T.A. Dorgan in Zwilling TAD Lex. (1993) 85: Owen Moran [...] met Tommy O’Toole at the National Athletic Club in Philadelphia Saturday night, and came in under wraps, as they say at the race track.
1921		H.C. Witwer Leather Pushers 6: This one to-night is only a stall for the real sugar, get me? Loughlin’s gonna be under wraps all the way.
1941		B. Schulberg What Makes Sammy Run? (1992) 67: She was dancing under wraps but looked as though she really enjoyed it.
1960		(con. 1940s) G. Morrill Dark Sea Running 27: He didn’t have the Old Man’s manner of great strength under wraps.
1979		D. Maitland Breaking Out 57: Kept it under bloody wraps. [...] Not a bloody word to anyone.
1989		J. Morton Lowspeak 143: Under Wraps – a horse ridden to give less than his best.
1995		D. Lodge Therapy (1996) 149: He wants to keep his private life under wraps.
2012		IOL Cape Western News (SA) 15 Feb. 🌐 The abuse of South African women by foreign nationals is apparently a huge problem that is kept under wraps.