Seek support (7)
'seek support' is the definition.
(as in to canvass for votes)
This is the entire clue.
(Other definitions for canvass that I've seen before include "Survey people for opinions" , "What politician may do" , "Search for support" , "Visit to ask for votes" , "Electioneer" .)
(Other definitions for woo that I've seen before include "Try to attract" , "Court, seek to marry" , "Court, romance" , "Do courting" , "Court (someone)" .)