Poor sap, possibly, left after marriage offer (8)
I believe the answer is:
proposal
'marriage offer' is the definition.
('proposal' can be a synonym of 'marriage offer')
'poor sap possibly left' is the wordplay.
'possibly' is an anagram indicator.
'left' becomes 'l' (common abbreviation).
'poor'+'sap'='poorsap'
'poorsap' is an anagram of 'proposa'.
'proposa'+'l'='PROPOSAL'
'after' is the link.
(Other definitions for proposal that I've seen before include "union offer?" , "A suggestion, perhaps of marriage" , "put before the union?" , "Offer (to get spliced?)" , "Plan, suggestion" .)