How to update data with a trigger function and a join
Just SET the value for field_1 BEFORE INSERT OR UPDATE.  Just, make sure you use the alias for the new row of data.

needs to be edited for postgresql syntax

CREATE TRIGGER trigger1
   BEFORE INSERT OR UPDATE 
   ON relation_b
   FOR EACH ROW
begin
  -- "new" represent "current row being inserted/updated"
  -- just modify the values BEFORE it is stored in the DB

  select a.field_1
    into new.field_1
  from relation_a a
  where a.id_a = new.fk_a;

  -- add exception handle where "no data is found"
end;