Draw green woodpecker striking head next to river (6)
I believe the answer is:
raffle
'draw' is the definition.
(a prize draw)
'green woodpecker striking head next to river' is the wordplay.
'green woodpecker' becomes 'yaffle' (term for the green woodpecker).
'striking head' means to remove the first letter (strike out or remove the first letter).
'next to' means one lot of letters go next to another.
'river' becomes 'r' (abbreviation for river).
'yaffle' with its initial letter removed is 'affle'.
'affle' after 'r' is 'RAFFLE'.
(Other definitions for raffle that I've seen before include "Lottery with goods as prizes" , "Lottery to win goods" , "charity event" , "Lottery with articles as prizes" , "Fund-raising draw" .)