Hi, Prakash.
You may use (MIM)Microsoft Identity Manager to perform a galsync between the forests.
It needs a SQL server in your environment.
About the detailed steps, you may refer to this article:
Using Microsoft Identity Manager Synchronisation Server's Global Address List Synchronisation feature to create a shared global address book across three Exchange Forests
(Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information. )
Once the galsync succeeded, you may see mailboxes in another forests synced in the specific OU and appear as "cross-forest mail contact" in EAC>contacts.
About configuring the free/busy(availability) service, there is also a Microsoft document: Configure the Availability service for cross-forest topologies
And since you are using Exchange 2013, there are some additional steps introduced in this KB: Cross forest free/busy lookup fails when target forest is Exchange Server 2013 or Exchange Server 2016
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