Primate mentioned briefly, dressing king (4)
I believe the answer is:
saki
'primate' is the definition.
(saki is a kind of primate)
'mentioned briefly dressing king' is the wordplay.
'mentioned' becomes 'said' (I've seen this before).
'briefly' means to remove the last letter.
'dressing' indicates putting letters inside (a dressing is a kind of covering).
'king' becomes 'k' (abbreviation for king in chess).
'said' with its final letter removed is 'sai'.
'sai' enclosing 'k' is 'SAKI'.
(Other definitions for saki that I've seen before include "drink in Tokyo" , "Japanese rice alcohol - British short story writer" , "Short-story writer" , "Pen name of short story writer, H.H. Munro, d. 1916" , "Japanese rice wine" .)