Correspond with Penny, say, not finishing drink (8)
I believe the answer is:
coincide
'correspond' is the definition.
(coinciding is a kind of corresponding)
'with penny say not finishing drink' is the wordplay.
'with' says to put letters next to each other.
'penny say' becomes 'coin' (penny is a kind of coin).
'not finishing' means to remove the last letter.
'drink' becomes 'cider' (cider is a kind of drink).
'cider' with its last letter removed is 'cide'.
'coin' put next to 'cide' is 'COINCIDE'.
(Other definitions for coincide that I've seen before include "Happen simultaneously" , "agree" , "Occur simultaneously" , "match" , "Correspond" .)