The most common and most likely answer to this crossword clue is the 10 letter word CONTROLLER
I've seen this crossword clue in The Daily Telegraph
C
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Buddy explains!
The straight part
We know that "Supervisor" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case supervisor = controller.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CONTROLLER mean?
CONTROLLER noun- One who controls something.
- Any electric or mechanical device for controlling a circuit or system.
- A person who audits, and manages the financial affairs of a company or government; a comptroller.
- A mechanism that controls or regulates the operation of a machine, especially a peripheral device in a computer.
- An iron block, usually bolted to a ship's deck, for controlling the running out of a chain cable. The links of the cable tend to drop into hollows in the block, and thus hold fast until disengaged.
- The person who supervises and handles communication with an agent in the field.
- The subject of a control verb. See Control (linguistics)
- In software applications using the model-view-controller design pattern, the part or parts of the application that treat input and output, forming an interface between models and views.