Men let gannet free in mix-up (12)

I believe the answer is:

entanglement

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'mix-up' is the definition.
Although both the answer and definition are singular nouns, I don't understand how one could define the other.

'men let gannet free' is the wordplay.
'free' indicates an anagram.
'men'+'let'+'gannet'='menletgannet'
'menletgannet' with letters rearranged gives 'ENTANGLEMENT'.

'in' is the link.

Can you help me to learn more?

(Other definitions for entanglement that I've seen before include "Confused state; perplexity" , "Ill-advised liaison" , "Imbroglio" , "A complication" .)

I've seen this clue in The Times.

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