Part of speech bishop added on short notice (6)
I believe the answer is:
adverb
'part of speech' is the definition.
(adverb is a kind of part of speech)
'bishop added on short notice' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'added on' is a charade indicator (letters next to each other).
'short' means to remove the last letter.
'notice' becomes 'advert' (notice can mean an advertisement).
'advert' with its last letter taken off is 'adver'.
'b' after 'adver' is 'ADVERB'.
(Other definitions for adverb that I've seen before include "Raved about book" , "Word to qualify an action" , "Word modifying adjective" , "Word as well, badly (gram.)" , ""Quickly" is one, for example" .)