Hello @Monica Manoharan and welcome to Microsoft Q&A. Thank you for your question.
There are multiple options available to accomplish this. My assumption is that you have 2 Data Factories, one for test, one for prod. The test Factory has a repository integration. The prod Factory does not need an integration.
Perhaps the easiest one, would be to leverage Azure Key Vault. You can have 2 Key Vaults, one for test, one for prod. Both should have the same secret names.
The idea is to have everything the same between the two Vaults, so all that needs to change is the Key Vault linked service base URL. This way, one change propagates through all the other linked services.
Other options include the CI/CD methods,
Manual promotion with parameterized template,
Global Variables and parameterized linked services