Face then run after the big cat (7)
I believe the answer is:
panther
'big cat' is the definition.
(panthers are big cats)
'face then run after the' is the wordplay.
'face' becomes 'pan' ('pan' is old-fashioned US slang for 'face').
'then' says to put letters next to each other.
'run' becomes 'r' (cricket abbreviation).
'after' means one lot of letters go next to another.
'r' put after 'the' is 'ther'.
'pan'+'ther' is 'PANTHER'.
(Other definitions for panther that I've seen before include "Then rap the large black cat" , "Black leopard" , "big pussycat" , "Big cat" , "kind of feline" .)