不予 is formal and official, used in legal, governmental, and bureaucratic contexts. In everyday speech, 不给 (bù gěi) or 不同意 (bù tóngyì) are used instead.
usage
Common collocations: 不予批准 (deny approval), 不予理会 (ignore), 不予受理 (refuse to accept a case), 不予置评 (decline to comment).