Dirty pal turning bishop into maiden (5)
I believe the answer is:
muddy
'dirty pal turning' is the definition.
'muddy' can be an answer for 'dirty' (muddying is a kind of dirtying). I am unsure of the 'pal turning' bit.
'bishop into maiden' is the wordplay.
'bishop' becomes 'DD' (DD stands for Doctor of Divinity).
'into' means one lot of letters goes inside another.
'maiden' becomes 'muy' (I can't explain this - if you can you should give a lot more credence to this answer).
'dd' going into 'muy' is 'MUDDY'.
(Other definitions for muddy that I've seen before include "Covered in mire" , "Not bright or clear" , "Slimy" , "Mucky, marshy" , "Bespattered" .)