Hi Geetika Talreja,
Welcome to Microsoft Q&A forum and thanks for using Azure Services.
As I understand, you want to perform incremental data load from one Azure Database Postgres SQL to another Azure Postgres SQL database.
For this purpose Azure Database Migration Service is not required, instead you can utilize Azure Data Factory for data movement.
Azure DMS is a fully managed service designed to enable seamless migrations from multiple database sources to Azure data platforms with minimal downtime (online migrations).
However, in your case both resources are on Azure Platform and we have connectors/Linked service for the Database.
Please refer to the Copy and transform data in Azure Database for PostgreSQL using Azure Data Factory or Synapse Analytics.
In the above document it is mentioned: Enable incremental extract: Use this option to tell ADF to only process rows that have changed since the last time that the pipeline executed.
Please go through it and let us know if you have any queries.
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Thank you.