Heartless guy went round edge thats dirty (5)
I believe the answer is:
grimy
'dirty' is the definition.
(I've seen this before)
'heartless guy went round edge' is the wordplay.
'heartless' suggests removing the centre.
'went round' means one lot of letters goes inside another (I've seen this in other clues).
'edge' becomes 'rim' (rim is a kind of edge**).
'guy' with its middle removed is 'gy'.
'gy' placed around 'rim' is 'GRIMY'.
'thats' is the link.
(Other definitions for grimy that I've seen before include "Dirty - soiled" , "filthy" , "Mucky" , "Besmirched" , "Ingrained with dirt" .)