No inclination to listen to school board (7)

I believe the answer is:

entrain

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'board' is the definition.
(entraining is a kind of boarding)

I can't explain the remainder of the clue.

(Other definitions for entrain that I've seen before include "Board carriage" , "Pop on the coach" , "Get on a rail service" , "board the Orient Express?" , "Put on board at the station" .)

I've seen this clue in The Times.

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