Indulging in fantasies to win over party on left (13)
I believe the answer is:
woolgathering
'indulging in fantasies' is the definition.
(woolgather can mean to daydream)
'over party on left' is the wordplay.
'over' means one lot of letters go next to another.
'party' becomes 'gathering' (I've seen this before).
'on left' becomes 'wool' (I can't explain this - if you can you should give a lot more credence to this answer).
'gathering' after 'wool' is 'WOOLGATHERING'.
'to win' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
(Other definitions for woolgathering that I've seen before include "Absent-mindedness" , "Daydreaming" , "may be dreamy" .)