Hmmh, an interesting idea. I suppose a career choice such as this - picking on The Law™ rather than easy targets - is a bit out of the ordinary, but not entirely unrealistic, if personal issues are involved (for those who actually consider their pilot a character of the game world, rather than just an immortal avatar of their own self).
For example, perhaps the pilot has had their parents killed by a particularly brutal bounty hunter, and/or grew up on a pirate outpost ... basically either starting out on the criminal side by virtue of their birth, or suffering from "police brutality" and the collateral damage of a heavy-handed approach at law enforcement. Such a character would surely grow to hate bounty hunters, even those who have high ideals of their own, and thus seek to dispense a bit of "personal justice" as a matter of vengeance.
I could see this make for an interesting backstory, especially due to the moral grey area involved. The killer could even be so deluded by their own actions that they are convinced they are doing "the right thing". Like a freedom fighter for the oppressed.
That being said, as for a name for this role ... I feel the most obvious and crystal-clear term would be
Copkiller
Alternatively, Assassin - depending on whether you'd want to place the focus of the character on doing the kill or getting paid for it.