Apparently not in a hurry here are you?

The fact you waited so long makes it more difficult.

You need to speak to the LL. You need to get an understanding of how the LL views the other party. If the LL sees the other party as your guest, then you need to evict them as the tenant LL statutes of your state require. If the other party is seen as your guest by the LL, then you are the other parties LL. Since you have waited so long to take action, you will need to evict them rather than haveing them removed as a trespasser.

If he is a holdover tenant, then you need to demand the LL remove them and let the LL know that if he does not remove the now trespasser, then you will take that as a reason to void your lease and look for another apartment.

The LL, if he sees this other person as a holdover tenant, is liable to have them removed. Since he is renting the apartment to only you, then the LL is required to provide you with what your lease contracts him to, which is the full unencumbered use of the apartment. If he cannot do this, then he cannot hold you to your lease.