  We study the entanglement islands and subsystem volume complexity
corresponding to the left/right entanglement of a conformal defect in
$d$-dimensions in Randall-Sundrum (RS) braneworld model with subcritical
tension brane. The left and right modes of the defect mimic the eternal black
hole and radiation system respectively, and the entanglement entropy between
the left and right modes follows an eternal black hole Page curve. We compute
the volumes corresponding to the left and right branes with preferred
Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the
subregion complexity of the black hole and the radiation states respectively.
An interesting jump in volume is found at Page time, where the entanglement
curve is saturated due to the inclusion of the island surfaces. We explain
various possibilities of this phase transition in complexity at Page time and
argue how these results match with a covariant proposal qualitatively.
