N.J. Stat. § 46:8-4
Whenever a lease shall be duly surrendered in order to secure a renewal thereof, a new lease made and executed by the chief landlord, shall, without the surrender of all or any of the under leases, be as good and valid, to all intents and purposes, as if all of the under leases had been surrendered at or before the taking of the renewal lease. Every person, in whom any estate for life or lives or for years shall, from time to time, be vested by virtue of such renewal lease, and his executors and administrators, shall be entitled to the rents, covenants and duties, and have like remedy for the recovery thereof, and the underlessees shall hold and enjoy the premises comprised in their under leases, as if the original lease, under and by virtue of which the under leases exist, had not been surrendered. The chief landlord shall have and be entitled to the same remedy by distress or entry upon the premises comprised in any such under lease, for the rents and duties reserved by the renewal lease, to the extent that the same do not exceed the rents and duties reserved in the original lease, as he would have had if the original lease had not been surrendered, or as he would have had if the under leases had been renewed under the renewal lease.
N.J.S. § 46:8-4