Omission from lover? Sigh tiredly! (9)
I believe the answer is:
oversight
'omission' is the definition.
(I know that oversight is a type of omission)
'from lover? sigh tiredly' is the wordplay.
'from' indicates a hidden word.
'OVERSIGHT' can be found hidden inside 'lover sigh tiredly'.
(Other definitions for oversight that I've seen before include "Slip-up" , "Failure to notice - blunder" , "Failure to notice - supervision" , "Failure to notice something" , "Carelessness" .)