Mistake made by a bishop in not speaking up (7)
I believe the answer is:
erratum
'mistake' is the definition.
(erratum is a kind of mistake)
'a bishop in not speaking up' is the wordplay.
'bishop' becomes 'rr' (abbreviation for Right Reverend**).
'in' indicates putting letters inside.
'not speaking' becomes 'mute' (I've seen this before).
'up' is a reversal indicator (in down clue: letters go upwards).
'a'+'rr'='arr'
'arr' inserted into 'mute' is 'mutarre'.
'mutarre' back-to-front is 'ERRATUM'.
'made by' is the link.
(Other definitions for erratum that I've seen before include "Typo" , "Mistake in book, etc" , "something wrong?" , "Printing error" , "Printing mistake" .)