The lease may read, that if tenants continue to live here after lease is up then original lease renews.  

I renewed my registration in November at the Plymouth RMV and it took me 5 minutes. 

Then when the lease renews, we raise the rent. 

They renew at the prevailing rates at end of term.

Julia Salazar has 2 bills in the NY Senate committee- one for Good Cause eviction and another that makes rent control apply to ALL apartments in ny state including an automatic lease renewal of 1 or 2 years.

A problem tenant threatening not to renew without concessions sounds like a self solving problem!

and I'm curious what the best route is to renew a lease? 

NJ has a serious "anti-eviction" statute that requires leases be renewed, but its been like that for decades with no draconian incremental changes like you would fear.

For context, when is your mortgage on your current home up for renewal?

I assume she's paying her rent, otherwise you'd be evicting her for non-payment of rent, rather than just notifying her that you're not renewing her lease.