TLDR: I'm sure there will be other people who say that if your players are "mature" enough or play the game the "right way" that you should let it play out in game. I disagree, I think you need to sit the player of the cleric down and come up with a resolution where she is no longer a member of the party, or no longer a cleric of Gruumsh.
Longer version:
I have a confession. I hate inter-party conflict that rises to the level of PVP or someone leaving the party. Either as a player or a DM. I have enough grief in my life, I want my games to be more-or-less harmonious. People play for different reasons but I don't allow PVP in my games which I think should be inevitable in this scenario.
I don't think everybody is always happy singing kum-ba-ya linked arm-in-arm trading happy smiley faces. But it does mean that as a DM I would never have allowed this situation. Some character concept just don't work in a group game. I don't allow evil characters, and if the PC is truly dedicated to Gruumsh, they are or are going to become evil. If they don't enforce the will of Gruumsh, they will not be a cleric for very long. It may not be true in all campaigns, but Orcs in my world are evil monsters, not misunderstood noble humans with a bad skin condition. There are no "neutral" clerics of Grrumsh, any more than there are good clerics of Lollth.
So how to deal with this? Well, at the very beginning I would have said "no" to the concept. Group cohesion is more important than implementing the vision for a specific NPC. That's not how you decided it, so now the question is what to do about it.
You could handle it in game. The cleric gets urges to enforce the will of Gruumsh (sow chaos and destruction, make all elves suffer painfully before dying). If she fights these urges the visions get more brutal and she starts to lose control, at times having to roll a progressively more difficult wisdom save to not attack the elf. If she continues to fight off the urge, at some point she no longer receives spells. Choose a new god or a new class. If she does give in to the will of Gruumsh, obviously the cleric and the elf are not going to be part of the same party any more. Worst case scenario, one of the PCs will be dead.
That's not very satisfactory to me. Some people may love it, all I can say is that I would not. So I would have a frank discussion out of game and ask the player(s) what the envision happening. I'd make it clear that sooner or later, a cleric of Gruumsh will try to kill the elf if they want to continue to be a cleric. When that happens the cleric becomes an NPC (I make it clear there is no PVP in my game).
So I'd ask the player how they want to play it out. Explain the mechanism I plan on implementing (the wisdom saving throws mentioned above), and get feedback. Sometimes as a DM you have to make calls that will upset a player. If you want to involve the elf player or the rest of the group at some point, that's up to you. But when I set up a game I make it clear ... if I think your character is violating the basic social cohesion that holds the group together, I'll give you a warning. Ignore the warning and your PC becomes an NPC, write up a new character.