I want to travel from Madinah to Islamabad on Saudi Airlines, trying to book ticket early to get economic price, but my passport will be received after renewal on August 20th. Can I book the ticket now on my old passport and update my my passport information once received new Passport?
Yes. Usually you can change the passport and validity (and other data). Often such data is not mandatory on booking time.
Just check carefully when you should put the definitive data. If there is advanced personal information which are sent to destination country. It can vary from few hours (so at checkin) to few days before departure.
Just you should be now careful on putting the correct name (which will be on the new passport). Changing names on tickets is much more difficult, also if it is just correcting transliteration or name correction (e.g. maiden name).