Make a mistake, ending in mate by bishop (3)
I believe the answer is:
err
'make a mistake' is the definition.
(I've seen this before)
'ending in mate by bishop' is the wordplay.
'ending in' says to take the final letters.
'by' says to put letters next to each other.
'bishop' becomes 'rr' (abbreviation for Right Reverend).
The last letter of 'mate' is 'e'.
'e'+'rr'='ERR'
(Other definitions for err that I've seen before include "Blunder" , "Go astray" , "Go wrong" , "Leave the straight and narrow" , "Make a wrong move" .)