How To Make Recursive Algorithm Without Using Large Amount Of Resources

How can I make a recursive algorithm in TSQL without using a large amount of resources?

New hires are put on a 6 month probation period, Their probation ends at the 6 month mark + sick time isnull(floor(sick_hours/8),0) they accrued during that 6 months. Their accrued sick days are added to the 6 month probation period to establish a new probation end date.

I then have to do the following loop:

1)Determine if any of the days between the original probation end date and the new probation end date have any weekend days or holidays for a particular employee.

2)If it does, I add those days to the new probation end date to create a newer probation end date.
a.I then go back up to step 1).

3)If it does not, I jump out of loop and look at the next employee on probation.

Note: I already have coding for determining number of sick days accumulated during an employee’s probation period. Recursive CTE? Recursive function? Other?