Are you expecting to see two doctors? Hiring new mandatory staff (doctors, trainers, and pr managers) replaces the previous staff and pays the outgoing staff a severance fee of what they would have been paid at the upcoming Monday economic update. Firing a mandatory staff will automatically re-hire a minimal (level 1) staff member of that role with a salary of $2,000 per week.
Hiring new optional staff (youth trainer, nutritionist, sports psychologist) will also replace your current one, if any. Firing optional staff does not replace them, and there are no minimal optional staff.