Tailor isn't providing cover for primate (5)
I believe the answer is:
loris
'primate' is the definition.
(I've seen this before)
'tailor isn't providing cover' is the wordplay.
'cover' indicates the answer is hidden within the clue (I've seen 'covering' mean this).
'LORIS' can be found hidden inside 'tailor isnt providing'.
'for' acts as a link.
(Other definitions for loris that I've seen before include "lemur" , "Slow-moving nocturnal primate" , "Short-tailed mammal" , "Small nocturnal primate" , "Nocturnal primate of Southeast Asia (usually slender or slow)" .)