Hi Ketki Naik
Sorry for the delayed response.
The historic data from the old tenant will remain in the old tenant and will not automatically migrate.
Moving or renaming any Azure Application Insights resource changes the resource ID. When the ID changes for a workspace-based resource, the data sent for the prior ID is accessible only when you query the underlying Log Analytics workspace. The data won't be accessible from within the renamed or moved Application Insights resource. Please refer the below document
In order to Move Application Insights, you need to move Log analytics workspace, which is associated with App Insights, because data will be stored in Log Analytics workspace.
Tenant to Tenant Migration is not possible, but if you want to Move Within the Tenant, please follow the below Article.
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