If existing CDT is updated, do we need to update Data store too in Test or other regions while deploying

Hello manikantasivasatishb8870,

You need to update the database structure and and upload the script along with the changed CDT. No need to deploy data store again if the object is already present in your higher environments.

There are two ways of doing it and there is no best or worst of them. It just depends on how much access you have and what is supported by your deployment methods. 

1. Update the CDT, add the CDT and DS in a package, deploy it, and then re-publish the DS on the target environment. 
2. Update the CDT, add it in the package, add the DB script in the package and deploy the package.