Afterthought about an American cat (4)
I believe the answer is:
puss
'cat' is the definition.
(I've seen this before)
'afterthought about an american' is the wordplay.
'afterthought' becomes 'ps' (ps stands for postscript).
'about' is an insertion indicator.
'an american' becomes 'us' (**).
'ps' placed around 'us' is 'PUSS'.
(Other definitions for puss that I've seen before include "Cat (abbr)" , "Pet" , "Moggie" , "Feline" , "Cat (informal)" .)