Cat turning up with parent (4)
I believe the answer is:
puma
'cat' is the definition.
(puma is a kind of cat)
'turning up with parent' is the wordplay.
'turning' says the letters should be written in reverse.
'with' says to put letters next to each other.
'parent' becomes 'ma' (ma is a kind of parent**).
'up' back-to-front is 'pu'.
'pu'+'ma'='PUMA'
(Other definitions for puma that I've seen before include "US wild cat" , "back from Argentina" , "South American carnivore" , "International rugby player" , "Large mountain cat" .)