On entering NY museum, number one ace gets obsession (9)

I believe the answer is:

monomania

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'obsession' is the definition.
(I've seen this before)

I cannot understand how the rest of the clue works.

(Other definitions for monomania that I've seen before include "Obsession with one thing" , "obsessive single-mindedness" , "Unhealthy preoccupation with one thing" , "Single-minded passion" .)

I've seen this clue in The Independent.

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