Bishop's neighbour announced time for rest? (5)
I believe the answer is:
night
'time for rest?' is the definition.
(people sleep at night)
'bishop's neighbour announced' is the wordplay.
'bishop's neighbour' becomes 'knight' (on a chess board).
'announced' indicates a 'sounds like' (homophone) clue.
'knight' is a homophone of 'NIGHT'.
(Other definitions for night that I've seen before include "Illumination needed now" , "A Hard Day's (the Beatles)" , "Time for bed" , "Time of darkness" , "See 8" .)