Here's the actual text from the proposal and where it fits into the existing law:

Proposed bill:

https://www.gencourt.state.nh.us/bill_status/billinfo.aspx?id=146&inflect=2

1 New Subparagraph; Termination of Tenancy; Expiration of Term. Amend RSA 540:2, II by inserting after subparagraph (g) the following new subparagraph:

(h) For a lease or tenancy the original term of which is 6 months or longer, or for a lease or tenancy the term of which is less than 6 months but which has been renewed for a total period of 6 months or longer, the expiration of the term of the lease or tenancy, provided that the landlord has provided the tenant with written notice at least 30 days in advance of the termination date of the lease term that the lease will not be renewed and that the tenant must vacate the rental property at the end of the lease term.

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That gets tacked on to:

https://www.gencourt.state.nh.us/rsa/html/lv/540/540-2.htm

II. The lessor or owner of restricted property may terminate any tenancy by giving to the tenant or occupant a notice in writing to quit the premises in accordance with RSA 540:3 and 5, but only for one of the following reasons: