Must zakat be paid on money that was previously saved and has now been spent, given that its zakat was not paid at that time?

For zakat (definition) to be obligatory on money, two conditions must be met: the passing of a full lunar year (hawl) and the wealth reaching the niṣāb (which is approximately equivalent to 85 grams of pure gold or 595 grams of pure silver). If you are certain that your wealth has reached the niṣāb and a full year has passed, then zakat becomes obligatory; otherwise, it does not. What was spent for sponsoring an orphan does not count as zakat because there was no intention of it being zakat. If zakat became obligatory and you did not pay it, then it is a debt upon you that you must pay whenever you are able to. You should hasten to pay it, along with repentance and seeking forgiveness, once you have the means.