A fault that makes me tired (7)
I believe the answer is:
'a fault' is the definition.
('demerit' can be a synonym of 'fault')
'makes me tired' is the wordplay.
'makes' indicates anagramming the letters.
'metired' anagrammed gives 'DEMERIT'.
'that' acts as a link.
(Other definitions for demerit that I've seen before include "Feature deserving censure", "Fault, defect", "Mark given for a fault", "Conduct that deserves censure", "Something deserving censure".)