I'm not a fan of immediately deleting an AD account after an employee or contractor leaves the company. I've found that it's best to disable for at least 30 days and then delete the disabled accounts 1-2 times a year.
There are a couple of reasons why you don't want to delete an account immediately:
1- Forensics. If your organization has a need to pursue legal action against an employee or contractor you will need the original account(SID).
2- Automated Tasks- Users, especially IT workers, tend to setup automated tasks to do thinks like run jobs, automate reports, recycle services, etc. Your going to be in a bind if you delete the user account before you realized there were complex jobs or tasks tied to the ID's. You can't simply recreate the account with the same name because the SID won't be the same and that's what the automated tasks look at not the visible name of the account.
If you disable first, you can always re-enable the account, change or recover the password, and your back in business until you get the job transitioned over to a legitimate service account.