Head runs out of school preserve (8)

I believe the answer is:

maintain

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'preserve' is the definition.
(I know that preserve can be written as maintain)

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for maintain that I've seen before include "Profess" , "Uphold, preserve" , "Keep up - carry on" , "Take the view or keep up repairs" , "Preserve or contend" .)

I've seen this clue in The Times and The Sunday Times.

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