What happens if my partner wants to keep working for the company after I buy them out?

This is possible, but it needs to be addressed as a separate employment or consulting arrangement, distinct from the sale of their shares. Buying out someone's ownership doesn't automatically define, extend, or end their working relationship with the company, so the two need to be documented independently. If they'll continue as an employee, ordinary employment terms apply, and it's worth being clear about role, compensation, and how their employment could end in future, especially since their dynamic with the remaining owner has now shifted from co-owner to employee.

It's also worth knowing that since 2021, most employee non-compete agreements are unenforceable in Ontario, though there's a specific exception that can apply where a seller becomes an employee of the purchaser as part of a business sale, which is directly relevant here and worth discussing with a lawyer if you want the departing partner-turned-employee bound by a non-compete going forward. Keep the buyout agreement and any employment arrangement as clearly separate documents.