Hi @Fareeha Sattar Shaikh Thank you for posting the question on this forum.
If you have an ARM template generated for your Logic App, you can use that to deploy the App on a different environment using a different account and various approaches such as CLI, PowerShell, Visual Studio etc. Please refer to Deploy Azure Resource Manager templates for Azure Logic Apps
Here is a reference on how you can Create Logic Apps using ARM templates. If you have an existing resource in the portal, you can export the ARM template for the resource through Azure portal or CLI or PowerShell. Here is a reference for the documentation - Use Azure portal to export a template If you do use this approach to generate the template, please make sure to test this before using it in Production as the template might be missing some password parameters.
Hope this helps. Please let us know if you have any further questions.
If the response helped, please do click Accept Answer and Yes for the answer provided. Doing so would help other community members with similar issue identify the solution. I highly appreciate your contribution to the community.