The alter table command lets you do quite a bit. But when it comes to
altering existing constraints, there is not much you can do. If you want to
add an on delete cascade to an existing foreign key constraint, you are
going to need two statements.
The first statement will drop the constraint and the second statement will
recreate it with the addition of the on delete clause. Furthermore, you'll
want to do this in a transaction to ensure the integrity of your data during
the transition between indexes.
Here is an example:
begin;
alter table orders
drop constraint orders_customer_id_fkey;
alter table orders
add constraint orders_customer_id_fkey
foreign key (customer_id)
references customers (id)
on delete cascade;
commit;