Day important for primate (6)
I believe the answer is:
monkey
'primate' is the definition.
(monkey is a kind of primate)
'day important' is the wordplay.
'day' becomes 'mon'.
'important' becomes 'key' ('key' can be similar in meaning to 'important').
'mon'+'key'='MONKEY'
'for' is the link.
(Other definitions for monkey that I've seen before include "Chile pine (the Araucaria tree)" , "See 10" , "Primate with a long tail" , "Type of wrench for a monkey" , "Medium-sized primate" .)