Sending an async notification to another database in PostgreSQL
If the other database has established a connection to the database to which you are connected and has issued a LISTEN, then you send a NOTIFY to it the same way you would send one to anything else using the NOTIFY/LISTEN interface.

If the other database has not volunteered to LISTEN, then NOTIFY is not the right tool for the job.  You could use dblink or FDW to insert records into a queue table on the other database.  Or, insert them into a local queue table, and have the other database fetch them when it wants to.