  Partial reduction is a Randall-Sundrum reduction for only part of the AdS
region between finite tension brane and zero tension brane. This is interesting
in AdS/BCFT where the AdS bulk contains a defect brane. We employ partial
reduction for a AdS bulk with a brane evolving as a $2d$
Friedmann-Robertson-Walker (FRW) cosmology and demonstrate the equivalence
between defect extremal surface and island formula for a large subregion fine
grained entropy in boundary CFT. We then move to higher dimensions and
demonstrate the existence of $4d$ massless graviton on AdS$_4$ brane in partial
reduction. We also propose a partial reduction for a $4d$ FRW cosmology at
defect brane and obtain the Newton constant by computing boundary entropy.
