Hi, @Sachin Agarwal Welcome to Microsoft Q&A thanks for posting your question.
Restore to a Separate subscription is not possible, link here
However, if you are using are SQL API we have intra account copy activity that can migrate the data within Cosmos DB.
Please check the below documents
https://learn.microsoft.com/en-us/azure/cosmos-db/how-to-container-copy
https://learn.microsoft.com/en-us/azure/cosmos-db/restore-account-continuous-backup
Regards
Geetha