If a lease is surrendered by the lessee and a new lease of the land comprised in the surrendered lease is granted to the lessee, the following provisions apply to any interest in the land noted on the surrendered lease at the time of the surrender:
(a) the interest must be noted on the new lease;
(b) unless varied, terminated or discharged, the interest applies to the new lease in the same way as it applied to the surrendered lease.