The hilt is wrought in the shape of a bow and arrow, with the pommel fashioned as arrow fletching, and the crossguard forming the limbs of the bow. This reflects the sigil of House Tarly - the huntsman.
While dining with his banished son Samwell, Randyll Tarly discovers that his partner Gilly is a wildling. Furious, Randyll points out Heartsbane, briefly explaining its history and stating that it will never go to Samwell.
Later that night, Samwell steals Heartsbane as he leaves Horn Hill with Gilly and her baby, intending to use the sword in his studies about Valyrian steel in the Citadel. It is among his effects when they arrive at the Citadel of the Maesters, heavily wrapped. After the death of his father and brother the sword would go to samwell rightfully.
In the books
In the A Song of Ice and Fire novels, Heartsbane has been in the possession of House Tarly for five hundred years. Like Ice, it is a two-handed greatsword. It is currently wielded by Lord Randyll Tarly and, like the lands and titles of House Tarly, will pass to Dickon Tarly after Randyll passes away.