Record finished after daughter rested (8)
I believe the answer is:
depended
'rested' is the definition.
(I've seen this before)
'record finished after daughter' is the wordplay.
'record' becomes 'EP' (abbreviation for extended play record).
'finished' becomes 'ended' ('end' can be a synonym of 'finish').
'after' says to put letters next to each other.
'daughter' becomes 'd' (genealogical abbreviation).
'ep'+'ended'='epended'
'epended' after 'd' is 'DEPENDED'.
(Other definitions for depended that I've seen before include "Was conditional" , "Rested" , "Relied or hung on" .)