Send part for actor as an afterthought (10)
I believe the answer is:
postscript
'an afterthought' is the definition.
(a PS in a letter)
'send part for actor' is the wordplay.
'send' becomes 'post' (synonyms).
'part for actor' becomes 'script' (a script includes an actor's role or part).
'post'+'script'='POSTSCRIPT'
'as' acts as a link.
(Other definitions for postscript that I've seen before include "part of letter" , "Addition to a letter" , "PS" , "Last added words" , "Extra lines" .)