Turned up with mother following big cat (4)
I believe the answer is:
puma
'big cat' is the definition.
(I've seen this before)
'turned up with mother' is the wordplay.
'turned' is a reversal indicator.
'with' says to put letters next to each other.
'mother' becomes 'ma' (ma can mean mother).
'up' written backwards gives 'pu'.
'pu'+'ma'='PUMA'
'following' is the link.
(Other definitions for puma that I've seen before include "Panther" , "Big cat" , "Cougar" , "American wild cat" , "back from Argentina" .)