Shattered president's heading off, showing fatigue (9)
I believe the answer is:
tiredness
'fatigue' is the definition.
('tiredness' can be a synonym of 'fatigue')
'shattered president's heading off' is the wordplay.
'shattered' indicates an anagram.
'heading off' means to remove the first letter.
'presidents' with its initial letter taken away is 'residents'.
'residents' is an anagram of 'TIREDNESS'.
'showing' acts as a link.
(Other definitions for tiredness that I've seen before include "7 (anag)" , "Weariness" , "That's liable to occur at midnight" , "Weary feeling" , "Residents in state of fatigue" .)