I am closing soon on my first house hack and first home ever. It is a great property in a great location, and I believe it will be a solid investment for me. I will be inheriting tenant who has been in the property for several years now and always pays rent on time. The only issue is that she is way under market rent and will greatly impact my returns for as long as she is still occupying my property. 

Her lease ends at the end of the year but she has an option to extend the lease for two more terms with only a small increase in rent which will still leave me with very low rents compared to the market. She has expressed interest in leaving at the end of the lease if she can find a house to buy but if she can't I would hate to be stuck with her for any additional terms. She is violating the lease in a few minor ways such as having two additional animals that aren't in the lease and a boyfriend who has moved in even though he is not on the lease.

I am willing to let her stay until the end of her current term this year despite these infractions, but once this term is over, I want either sign a new lease with her or find a new tenant who will pay current market rents.

So my question is, are these infractions grounds to not honor the existing lease should she choose to exercise her extension clause once this current term comes to an end? If so, do I just refuse to extend the lease and how do I go about doing that?

Thank you for any advice.