A record broken by half-cut sleuth in bed, perhaps (6)
I believe the answer is:
asleep
'in bed perhaps' is the definition.
(people usually sleep in beds)
'a record broken by half-cut sleuth' is the wordplay.
'record' becomes 'EP' (abbreviation for extended play record).
'broken by' means one lot of letters goes inside another.
'half cut' suggests halving the letters.
'a'+'ep'='aep'
'sleuth' cut in half is 'sle'.
'aep' going around 'sle' is 'ASLEEP'.
(Other definitions for asleep that I've seen before include "Please be at rest, oddly" , "Elapse (anag)" , "Snoozing" , "Please be at rest (6)." , "See, pal strangely is not awake" .)