Neighbourhood facility in doubt, briefly (7)
I believe the answer is:
quarter
'neighbourhood' is the definition.
(I've seen this before)
'facility in doubt briefly' is the wordplay.
'facility' becomes 'art' (I've seen this in another clue).
'in' is an insertion indicator.
'doubt' becomes 'query' (I've seen this before).
'briefly' means to remove the last letter.
'query' with its last letter taken off is 'quer'.
'art' going into 'quer' is 'QUARTER'.
(Other definitions for quarter that I've seen before include "Fourth; mercy" , "See 17 Across" , "three months" , "Cut in four" , "deadly action after draw?" .)