There isn't.
If you want to play a vampire with a hunter background, you an simply play a vampire and add traits like turned hunter and some such. The results would be the same.

Alternatively you can start as a normal vampire and embrace a Hunter. After that you either try to kill your vamp so your Hunter childe inherits or you land yout childe and switch charakters. The only problem with this approach is that it might be difficult to actually encounter a hunter and I don't know if there are any event Hunter charcters beside Karl Schreckt.

Razogorth, there are many hunter characters on the Dark Ages Inquisitor bookmark

for RP purposes u could embrace a hunter, can even be a custom character u created with another mod that lets u make custom characters and then go into torpor to play as emm

a werewolf hunter that gets turned you say? get ready to roll the dice

There is no hunter in world of darkness who seeks to be embraced. They are carefully screened and vigorously trained/indocrinated to become sworn enemeis to vampires. Being embraced is not defeat, it's crashing humiliating defeat.

Basically what you ask for is playing to lose to be rewarding. It's utterly wrong I think. If you play poorly and get dethroned or conquered you can of course switch to your betters and pretend to be them from now on, but I think it's important that it does not happen automatically, to make it clear that you've lost and it sucks to be you.