Office a Tory left, sacked after a month (9)
I believe the answer is:
mayoralty
'office' is the definition.
(office or position of a mayor)
'a tory left sacked after a month' is the wordplay.
I cannot really understand how this works, but
'a' is found in the answer.
'tory' could be 'r' (abbreviation for right) and 'r' is found within the answer.
'left' could be 'al' (I've seen this in other clues) and 'al' is found in the answer.
'month' could be 'm' (standard abbreviation) and 'm' is located in the answer.
This may be the basis of clue (or it may be nonsense).
(Other definitions for mayoralty that I've seen before include "elected office" , "Henchard's office" , "public office" , "civic office" , "political office" .)