In general, and in particular in New Jersey, a new owner takes possession subject to existing rental agreements, and in particular subject to existing leases, unless there is a provision in the lease to the contrary. This happens automatically, by law. Thus any lease is as enforceable against the new owner as it would have been against the old.
But how enforceable is this arbitration agreement? How enforceable would it have been against the old owner O?
The basic fact about a month-to-month tenancy is that either party may end it on one month's notice, for any reason or none. Moreover, when a new owner intds to occupy the premises personally, or use them for his or her family, the requirement to honor a previous lease is, in general, not applicable.
T might be able to force N to go through arbitration, depending on the wording of the agreement, and on whether the written lease applies at all after the end of the first year (which it may well not). But on the facts as stated in the question, T would lose in arbitration as well as in court, and if there is any increased expense because of the arbitration, T would be obliged tom pay it.
Let us look at the actual NJ law
N.J.S.A. 2A:18-53 provides that:
any lessee or tenant at will or at sufferance,
or for a part of a year, or for one or more years, of any houses, buildings, lands or tenements, ... may be removed from such premises by the Superior Court,
Law Division, Special Civil Part in an action in the following cases:
a. Where such person holds over and continues in possession of all or any part of the demised premises after the expiration of his term, and after demand made and written notice given by the landlord or his agent, for delivery of possession thereof. The notice shall be served either personally upon the tenant or
such person in possession by giving him a copy thereof or by leaving a copy of the same at his usual place of abode with a member of his family above the age of 14 years. [emphasis added]
Section 2A:18-56 provides that:
No judgment for possession in cases specified in paragraph "a." of section 2A:18-53 of this Title shall be ordered unless:
a. The tenancy, if a tenancy at will or from year to year, has been terminated by the giving of 3 months' notice to quit, which notice shall be deemed to be sufficient; or
? b. The tenancy, if a tenancy from month to month, has been terminated by the giving of 1 month's notice to quit, which notice shall be deemed to be sufficient; [emphasis added]
Section 2A:18-57 provides that:
If no sufficient cause is shown to the contrary when the action comes on for trial, the court shall issue its warrant to any officer of the court, commanding him to remove all persons from the premises, and to put the claimant into full
possession thereof, and to levy and make the costs out of the goods and chattels of the person in possession.
No warrant of removal shall issue until the expiration of 3 days after entry of judgment for possession, except as provided for in chapter 42 of this Title.
Section 2A:18-61.1 provides that:
No lessee or tenant or the assigns, under-tenants or legal representatives of such lessee or tenant may be removed by the Superior Court from any house, building, mobile home or land in a mobile home park or tenement leased for
residential purposes, other than (1) owner-occupied premises with not more than two rental units or a hotel, motel or other guesthouse or part thereof rented to a transient guest or seasonal tenant; ... except upon establishment of one of the following grounds as good cause ... [emphasis in original]
h. The owner seeks to retire permanently the residential building or the mobile home park from residential use or use as a mobile home park
But note that good cause is not required for an owner-occupied dwelling with no more than two rental units.
T would be wise to consult a lawyer knowledgeable about landlord/tenant law in NJ before attempting to contest the notice or eviction.