Censor play, suffering drowsiness (10)
I believe the answer is:
narcolepsy
'drowsiness' is the definition.
'censor play suffering' is the wordplay.
'suffering' indicates an anagram.
'censor'+'play'='censorplay'
'censorplay' is an anagram of 'NARCOLEPSY'.
(Other definitions for narcolepsy that I've seen before include "Sleeping sickness" , "Dropping off at any time" , "dropping off unexpectedly?" , "dropping off complaint" , "Sleep disorder" .)