Dog is shy round the heartless (6)
I believe the answer is:
coyote
'dog' is the definition.
(I've seen this before)
'shy round the heartless' is the wordplay.
'shy' becomes 'coy' (coy can mean shy or modest).
'round' becomes 'o' (o is a circular letter).
'heartless' suggests removing the centre.
'the' with its middle removed is 'te'.
'coy'+'o'+'te'='COYOTE'
'is' acts as a link.
(Other definitions for coyote that I've seen before include "American prairie dog" , "US wild dog" , "Small N. American wolf" , "Confines" , "Small wild dog" .)