There are lots of ways to approach a problem like this.

The first one is to avoid it entirely: add code to whatever’s writing to the SQL Server database to either write to the Postgres DB directly, or to invoke an API / send an event / etc that does the write to Postgres.

Another option would be to use an off-the-shelf Change Data Capture (CDC) tool for SQL Server to (again) send changes to a system you build that writes to Postgres.

Since you’re discarding data that’s written from the Postgres side, yet another option would be a Foreign Data Wrapper (FDW) that allows Postgres to query the SQL Server DB from Postgres. For instance, the Postgres docs call out tds_fdw specifically for SQL Server.