Obsessive and uninspiring bishop dismissed (4)
I believe the answer is:
anal
'obsessive' is the definition.
(anal can mean obsessed with order)
'uninspiring bishop dismissed' is the wordplay.
'uninspiring' becomes 'banal' (I've seen this before).
'bishop' becomes 'B' (abbreviation for bishop in chess).
'dismissed' indicates named letters should be taken away.
'banal' with 'b' taken out is 'ANAL'.
'and' acts as a link.
(Other definitions for anal that I've seen before include "Excessively orderly and fussy" , "Obsessive" .)