First things first, define your project, its scope, genre, the style, limitations, your budget and your capabilities. What is this game you want to develop? What is the main purpose of this game: just to entertain users, or something else? What is the target audience? What tech stack do you prefer?
Secondly, define the model of collaboration that suits you the most? Do you want your outsourcing partner to develop a game from scratch for you? Or you want to engage their team and collaborate on the development together? Or maybe you just need the extra hands of a few specialists?
When looking for your possible external partner, pay attention to their proven track record, case studies, previous projects, clients reviews, portfolios, and communication style.
Assign them a series of interviews, evaluating their technical knowledge, management style, adherence to methodologies like Waterfall, Scrum or Agile.
Pay close attention to how they communicate with you, are they transparent enough, are they collaborative and open to feedback. All these factors influence your future partnership.