1
general::
Refuse to talk or respond, as in Whenever she asks her teenager about his activities, he clams up. This term alludes to the tightly closed valves of a live clam. [Slang; early 1900s]
American Heritage Idioms
2
general::
Phrase(s): clam up
to say nothing. (Closing one’s mouth in the way that a clam closes up.) • The minute they got him in for questioning, he clammed up. • You’ll clam up if you know what’s good for you.
McGrawhill's American Idioms And Phrasal Verbs