Does your character have the Echo?
If YES: She could approach the Scions of the Seventh Dawn, likely via the Sons of Saint Coinach or another academic contact, and ask to be allowed to participate in a future defeat of a primal. OR: If she knows she's immune to tempering, then she might have the confidence to place herself in a position where she'll be kidnapped for tempering by a primal's followers. There's still the very likely chance the primal would kill her, though, if she was going in alone.
If NO: Bit trickier. Tristan's backstory seems to imply the Immortal Flames, at least, have a "primal-killing squad" who are dispatched whenever a new incarnation of Ifrit is summoned. I can only imagine the other grand companies have similar squads... who are basically suicide troops. Everyone is always VERY reluctant to go to battle with a Primal, because if they aren't killed, there's a high likelihood they'll be tempered/drowned/etc and THEN killed. By their own people. Out of necessity. Primal battles are always very high casualty for people without the Echo. I can only imagine someone actively asking to join one of these suicide squads would be viewed with "uh, why, we need you elsewhere" and/or "sure if that's what floats your boat", depending on the exact commanding officer, how well-known the character is to the grand company, and other factors.
That's my take on it anyway!
If YES: She could approach the Scions of the Seventh Dawn, likely via the Sons of Saint Coinach or another academic contact, and ask to be allowed to participate in a future defeat of a primal. OR: If she knows she's immune to tempering, then she might have the confidence to place herself in a position where she'll be kidnapped for tempering by a primal's followers. There's still the very likely chance the primal would kill her, though, if she was going in alone.
If NO: Bit trickier. Tristan's backstory seems to imply the Immortal Flames, at least, have a "primal-killing squad" who are dispatched whenever a new incarnation of Ifrit is summoned. I can only imagine the other grand companies have similar squads... who are basically suicide troops. Everyone is always VERY reluctant to go to battle with a Primal, because if they aren't killed, there's a high likelihood they'll be tempered/drowned/etc and THEN killed. By their own people. Out of necessity. Primal battles are always very high casualty for people without the Echo. I can only imagine someone actively asking to join one of these suicide squads would be viewed with "uh, why, we need you elsewhere" and/or "sure if that's what floats your boat", depending on the exact commanding officer, how well-known the character is to the grand company, and other factors.
That's my take on it anyway!