A bishop comes in at this time, tight (6)
I believe the answer is:
narrow
'tight' is the definition.
(thesaurus)
'a bishop comes in at this time' is the wordplay.
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'comes in' means one lot of letters goes inside another.
'at this time' becomes 'now' (I've seen this before).
'a'+'rr'='arr'
'arr' placed inside 'now' is 'NARROW'.
(Other definitions for narrow that I've seen before include "Small-minded" , "Fine" , "Cramped" , "Strict" , "Keen" .)