Puzzle brings comfort in district's centre (6)
I believe the answer is:
teaser
'puzzle' is the definition.
(I've seen this before)
'comfort in district's centre' is the wordplay.
'comfort' becomes 'ease' (synonyms).
'in' is an insertion indicator.
'centre' means to look at the middle letters.
The middle of 'district' is 'tr'.
'ease' going into 'tr' is 'TEASER'.
'brings' is the link.
(Other definitions for teaser that I've seen before include "Difficult question" , "one using a backcomb" , "One who annoys people or cards wool" , "Introduction to arouse curiosity" , "inducement" .)