She has her own little side quest that ends up with you at a snow covered place , you can get to there through the haunted forest, which you can get to through a portal in the paradox zone, first you need to talk to her in the same town as Deino's diner
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She has her own little house in New Alexandria with a wooden sign next to the door, once you talk to her, you have to go to Deino's dinner first to grab something and then return to her. After that I think it's pretty straight forward, head to the frozen ruins location and meet up with her. You will then be told you need to catch a specific Pokémon that has 3 types. (You need to get very far in the game to find the Pokémon you need) Once you return to Emma at the frozen ruins with the pokemon, you will then be able to catch Emma (It's very easy to shiny hunt her, there is an NPC in the school that can tell you how to shiny-chain pokemon using vore moves, same room where you buy pred balls) After that the mini side quest ends and you will now have Emma to use in your party.