@Gaurav Singh Gagwari
Here’re steps:
1.Use an account with these memberships.
(1)securityadmin fixed server role on the SQL Server instance
(2)db_owner fixed database role on all databases that are to be updated
(3)administrators group on the server on which you are running the PowerShell cmdlets
2.Stop search service by using PowerShell.
$ssa = Get-SPEnterpriseSearchServiceApplication -Identity <SearchServiceApplicationName>
Suspend-SPEnterpriseSearchServiceApplication -Identity $ssa
3.Back up search service application in the SharePoint 2013.
Reference:
Back up search service application in SharePoint Server.
4.Restore search service application in the SharePoint 2016.
Restore search service application in SharePoint Server.
5.Create a search service application with restored database in the SharePoint 2016.
If an Answer is helpful, please click "Accept Answer" and upvote it.
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.