Dubious activity of primate disturbing current king (5)
I believe the answer is:
caper
'dubious activity' is the definition.
'caper' can be an answer for 'activity' (caper is a kind of activity). I am not certain of the 'dubious' bit.
'primate disturbing current king' is the wordplay.
'primate' becomes 'ape' (large primate).
'disturbing' indicates putting letters inside (inserted letters disrupt or disturb the word).
'current king' becomes 'cr' (short for Carolus Rex, King Charles in Latin. I am not sure about the 'current' bit.).
'ape' put inside 'cr' is 'CAPER'.
'of' acts as a link.
Can you help me to learn more?
(Other definitions for caper that I've seen before include "Pickled flower bud or prank" , "Dance; pickled bud" , "game" , "Run about playfully, frolic" , "One likely to get pickled" .)