Dismiss Part-Time for Full-Time
In short, yes. Generally, you need to be able to show that the requirements for the position have changed to the point where it requires 40 hours per week and that hiring another part-time resource to job share is not a viable option. You also should then offer the full-time role to the part-time incumbent. If they are unable / unwilling to accept the new role, then you generally can proceed with your plans to replace the employee. Consult an expert prior to doing this as there are several areas of potential liability to manage.