PostgreSQL custom domain with trigger Is it possible to create custom domain / data type and associate some trigger with it, for example hash password?

I will have for example password domain and if I set some value to this column, it will automatically hash that, so I don't have to create trigger for each table with password column
You cannot do that.

As the documentation says:


  CREATE TRIGGER creates a new trigger. The trigger will be associated
  with the specified table or view


This clearly excludes types and domains.  (Very logically: triggers are normally fired upon changing something - here you want to change a column, not the type.)

You should instead use a stored procedure to take care of your password column(s).  And personally I think the less places password are stored at, the better.