Green’s Dictionary of Slang

silent, discreet, refusing to talk.

1936		R. Chandler ‘Goldfish’ in Red Wind (1946) 167: Think he’ll stay clammed?
1942		R. Chandler High Window 134: Even if I had the legal right to stay clammed-up – refuse to talk – and got away with it once, that would be the end of my business.
1990		(con. early 1950s) J. Ellroy L.A. Confidential 147: And our suspects are clammed, and Bud White killed the one witness who could have helped us.
2001		J. Baker Shooting in the Dark (2002) 107: Christ, you say guys are all clammed up and they don’t know how to relate to their emotions.
2004		E. Weiner Drop Dead, My Lovely (2005) 153: She was clammed and clamped and we were getting nowhere.