Organiser may show irritation having to support a bishop (8)
I believe the answer is:
arranger
'organiser' is the definition.
(I know that organiser can be written as arranger)
'irritation having to support a bishop' is the wordplay.
'irritation' becomes 'anger'.
'having to support' is a charade indicator (letters next to each other) (some letters go underneath or support others).
'bishop' becomes 'rr' (abbreviation for Right Reverend).
'a'+'rr'='arr'
'anger' put after 'arr' is 'ARRANGER'.
'may show' acts as a link.
(Other definitions for arranger that I've seen before include "Musician" , "One who adapts music" , "Rare gran (anag.)" , "Orchestrator" , "Organiser" .)