Re: How I can make the trigger calculates the sum of a column for specific condition

[Peter Brawley]

debt_alert.salary_transaction_id references salary_transactions.salary_transaction_id, on insert to which there can thus be no existing referring debts, so all you need is ...

create trigger remaining_money_calc
after insert on salary_transaction for each row 
insert into debt_alerts set
  salary_transaction_id = NEW.salary_transaction_id,
  remaining_money = 0, 
  employee_id=NEW.employee_id;

In an update Trigger there could be a need to do such a sum; you'd condition it on ...

...where salary_transaction_id=NEW.salary_transaction_id...

A note on Trigger naming ... to facilitate maintenance, it's a good idea to adopt a naming convention and stick to it. My preference is table_name_operation_context, so if it's my Trigger, its name is something like t_ins_money.