Promise to return the record and move on (6)
I believe the answer is:
pledge
'promise' is the definition.
(I know that pledge is a more specific form of the action promise)
'return the record and move on' is the wordplay.
'return' is a reversal indicator.
'the record' becomes 'L-P' (abbreviation for long play record).
'and' says to put letters next to each other.
'move on' becomes 'edge' (edging is a kind of moving on).
'lp' written backwards gives 'pl'.
'pl'+'edge'='PLEDGE'
'to' is the link.
(Other definitions for pledge that I've seen before include "assurance" , "Promise solemnly and formally" , "make toast" , "Promise or pawn" , "Promise, word of honour" .)