Mistake made by Eastern bishop getting nothing right (5)
I believe the answer is:
error
'mistake' is the definition.
('error' can be a synonym of 'mistake')
'eastern bishop getting nothing right' is the wordplay.
'eastern' becomes 'e'.
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'getting' is a charade indicator (letters next to each other).
'nothing' becomes 'o' (looks like zero - 0).
'right' becomes 'r' (common abbreviation).
'e'+'rr'+'o'+'r'='ERROR'
'made by' acts as a link.
(Other definitions for error that I've seen before include "Boob" , "Bloomer, blunder" , "Slip, mistake" , "heresy" , "Faux pas" .)