Is zakat obligatory on entrusted money that has reached the nisab and upon which a year has passed, and it is impossible to contact its owner to seek permission for its disbursement?

Zakat is not to be disbursed from deposited money except with the owner's permission, because it is a condition for Zakat that the money be fully owned. The one holding the deposit is not permitted to disburse Zakat from the deposit without the owner's permission.