Old heartless Richard III in feud about filth (6)
I believe the answer is:
ordure
'filth' is the definition.
(I've seen this before)
'old heartless richard iii in feud' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'heartless' suggests removing the centre.
'iii in feud' becomes 'ure' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'richard' with its centre removed is 'rd'.
'o'+'rd'+'ure'='ORDURE'
'about' is the link.
(Other definitions for ordure that I've seen before include "Dirt" , "soil" , "Excrement" , "unclean" , "Dung, filth" .)