The tenant does not have to leave the unit because he is on a short term tenancy. Once the short term lease ends, it renews automatically on a month-to-month basis according to the law.  Your recourse is to serve your tenant with Form N4. This notice gives the tenant 14 days to pay the rent arrears. If the tenant does not pay within the specified time, a landlord may file an application with the Landlord and Tenant Board for termination and an eviction order.

In terms of the shared expenses, if these pertain to unpaid utilities, you need to serve your tenant with Form N5. This notice gives the tenant 7 days to pay the utilities. If the tenant does not pay within the 7 days, you can also file an application with the Landlord and Tenant Board for an order to evict the tenant and collect the utility costs.