Direct supervisor means the person to which the Employee directly reports and who supervises the Employee's work on a regular basis.

Honestly, I have never heard it with "direct". So just supervisor should be fine. This title generally places somewhere between direct report (subordinate) and manager and act as a bridge.

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Note added at 22 mins (2021-11-16 17:15:38 GMT)
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Bu da HR perspektifinden tanımı:

https://hr.tulane.edu/content/direct-supervisors-and-delegat...

"Immediate supervisor" kullanımı oldukça yaygın.

Bu kişiye bağlı çalışanlar ise "direct reports" olarak kullanılıyor.

Immediate Supervisor. That person in an administrative or supervisory position directly responsible for the supervision and direction of an employee and to whom the employee is directly responsible.

Böyle kullanıyorum.