Any employee ID of ex-employees should ideally not be given to any new employees. Almost all corporates do not allocate the employee IDs of their former employees to their new employees.
Issues with Reallocating Employee IDs
The major issues that can arise if you allocate the old employee IDs to a new employee are that when working on employee data for any reference, you or the software you are using (if applicable) will not be able to get proper and accurate information about the employee. There is a possibility of clashes of employee IDs. In case you are using software, the software itself will not allow you to allocate the old employee ID to a new employee.
Therefore, I suggest that you allocate a new employee ID to every new employee, categorizing it in serial order.
Hope I have cleared your doubt.
Regards