Repeatedly annoy them with poorly executed Irish dance which was later cut in rehearsals (6)

I believe the answer is:

harass

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'repeatedly annoy' is the definition.
'harass' can be an answer for 'annoy' (harassing is a kind of annoying). I am unsure of the 'repeatedly' bit.

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for harass that I've seen before include "Harry" , "Pester, badge" , "Annoy persistently, persecute" , "Pester constantly" , "Persistently pester" .)

I've seen this clue in The Irish Times.

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