Refuse to twist neck (4,4)
I believe the answer is:
turn down
'refuse' is the definition.
(to turn down an offer is to refuse it)
'twist neck' is the wordplay.
'twist' becomes 'turn' (synonyms).
'neck' becomes 'down' (both can mean to swallow or drink quickly).
'turn'+'down'='TURN-DOWN'
'to' is the link.
(Other definitions for turn down that I've seen before include "Spurn" , "Reject - reduce volume" , "mark the place" , "Refuse - to reduce the volume" , "prepare bed" .)