adjective

careful and prudent in one’s speech or actions, especially in order to keep something confidential or to avoid embarrassment.

we made some discreet inquiries

careful,circumspect,cautious,wary,chary,guarded,close-lipped,close-mouthed,tactful,diplomatic,considerate,politic,prudent,judicious,strategic,wise,sensible,delicate,kid-glove,softly-softly