Gasp at that woman being a cougar? (7)
I believe the answer is:
panther
'a cougar?' is the definition.
(synonyms)
'gasp at that woman' is the wordplay.
'gasp' becomes 'pant' (synonyms).
'at' means one lot of letters go next to another.
'that woman' becomes 'her' (pronoun for a woman).
'pant'+'her'='PANTHER'
'being' acts as a link.
(Other definitions for panther that I've seen before include "big pussycat" , "kind of feline" , "See 2" , "Black leopard" , "Bagheera?" .)