Putting a constraints on a already made table in PostgreSQL
Tables don't have "variables" - they have columns. 

But yes, you can change an existing column to NOT NULL:

alter table existing_table
   alter  the_column set not null;


Note that this will fail, if the column contains NULL values. In that case you need to first update all NULL values to something different, before you can run that statement.

See the manual for more examples. 



Another option is to use a check constraint, which allows you to name the constraint:

alter table existing_table
  add constraint check_column_not_null check (the_column is not null);