Inclined to secrecy or reticence about divulging information(adjective)
WordNet. Princeton University. 2010.
Use "closelipped" in a sentence
"If contact is to be made it must come from the specialists, the encoders and analysts who have sat silent and waited, stern and closelipped, for more input."
"It's over quickly, just as you're still admiring Branagh's closelipped way with a line; Julia Ormond's sweetly melancholy Vivien Leigh seeing dailies with Olivier - to whom she was married at the time - she's moved, sadly, by Marilyn's beauty; Emma Watson as an ever-so-slightly jaded young wardrobe girl; and Judi Dench as legendary actress Dame Sybil Thorndike, presented here as the kindest and gentlest of colleagues."