Cat hair covering wig, trimmed at the front (7)
I believe the answer is:
tigress
'cat' is the definition.
(I know that tigress is a type of tiger)
'hair covering wig trimmed at the front' is the wordplay.
'hair' becomes 'tress' (tress is a kind of hair).
'covering' is an insertion indicator.
'trimmed at the front' means to remove the first letter.
'wig' with its first letter taken off is 'ig'.
'tress' enclosing 'ig' is 'TIGRESS'.
(Other definitions for tigress that I've seen before include "Female wildcat" , "Large she-cat" , "Wild cat (female)" , "Wild animal" , "Fierce woman" .)