Basically, don't. While it's possible it's probably a poor idea simply because SQL is multiuser so in production unless you are really, really careful it's far too easy to generate duplicate values.
You can get it right by not trying to increment anything yourself.
Use an internal ID - IDENTITY is fine - to give every employee a sequential number. Link the employee to the department via a foreign key. Make the DepartmentID the "short sequence" so they don't get duplicated.
Then create a stored procedure to add your user.
INSERT the base data, then use a SELECT to find all the employees in the same department, and use ROW_NUMBER
] to get the employee number in the department from the IDENTITY value you just created by INSERTing.