Not smart to send up bishop with slander (4)
I believe the answer is:
dumb
'not smart' is the definition.
(I've seen this in another clue)
'send up bishop with slander' is the wordplay.
'send up' is a reversal indicator.
'bishop' becomes 'B' (chess abbreviation).
'with' says to put letters next to each other.
'slander' becomes 'mud' (as in to drag someone's name through the mud).
'b'+'mud'='bmud'
'bmud' written backwards gives 'DUMB'.
'to' acts as a link.
(Other definitions for dumb that I've seen before include "Stupid; unable to speak" , "Silent" , "Thick" , "Mute" , "Not able to speak" .)