Drill might vex them (8)

I believe the answer is:

exercise

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'drill' is the definition.
(I know that drill can be written as exercise)

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for exercise that I've seen before include "Task for pupil" , "that every prisoner should have" , "Task performed to develop skill" , "Do it to develop skill or fitness" , "Workout" .)

I've seen this clue in The Irish Times.

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