display a ‘*’ against a row

You are performing that select max(hireddate) for each and every row where you only need to do this once.

Anything in the select sector of a query will be evaluated for each row
Anything in the from sector is assessed only once.

You could asses the date before hand and compare to that. Date fields a pretty efficient for indexing as sorting
But there is another way for working with aggregates: Common Table Expressions (CTE)

you can predefine a table that is assessed only when it is used in the query. This makes for an efficient ordering and selecting template:

with my_cte as ( -- define the cte
select EmployeeId,Row_Number() over (order by HireDate desc) as row
from Employment
) -- must be followed by another cte or a select statement
SELECT  
	EmployeeName + -- You can swap your case select to make it look a little neater
            CASE row WHEN 1 then '*' else '' end AS EmployeeName, 
	EmployeeNo , 
	HireDate
FROM 
	Employment e
inner join my_cte on e.EmployeeId= my_cte.EmployeeId

The reason I would always run to a cte is because of how useful is can be with these kind of aggregates
For example: Say we now want the most recent employee hire from each department to have a * we can alter the cte ROW_NUMBER like so:

with my_cte as ( -- define the cte
select EmployeeId,Row_Number() over(PARTITION BY department order by HireDate desc) as row
from Employment
) 

This change has the effect of resetting the row numbering for each department so each of the departments latest employee would show the *

Alternatively, you could perform your select in the from sector:

SELECT  
	EmployeeName + 
		CASE
			WHEN HireDate = aggregatevalue.date THEN  ' *'
			ELSE '' 
		END AS EmployeeName, 
	EmployeeNo , 
	HireDate
FROM 
	Employment,
		(
	SELECT 
		Max(HireDate) as date
	FROM 
		Employment
	) as aggregatevalue

there is no table join but the aggregate table will only have 1 row so it won't be a problem