Primate kept secret about love with minister (7)
I believe the answer is:
hominid
'primate' is the definition.
(hominid is a kind of primate)
'kept secret about love with minister' is the wordplay.
'kept secret' becomes 'hid' (I've seen this in another clue).
'about' is an insertion indicator.
'love' becomes 'o' (love means zero in tennis).
'with' means one lot of letters go next to another.
'minister' becomes 'min' (abbreviation).
'o'+'min'='omin'
'hid' placed around 'omin' is 'HOMINID'.
(Other definitions for hominid that I've seen before include "Member of zoological family of humans and ancestors" , "Fossil human" , "Any extinct ancestor of man" , "Old man" , "Man or manlike creature" .)