The rabbit, shy, keeps out of the way (5)

I believe the answer is:

coney

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'the rabbit' is the definition.
(synonyms)

'shy keeps out of the way' is the wordplay.
'shy' becomes 'coy' (I've seen this before).
'keeps' is an insertion indicator.
'out of' becomes 'n' (I can't explain this - if you can you should believe this answer much more).
'the way' becomes 'e' (Compass direction - East).
'n'+'e'='ne'
'coy' going around 'ne' is 'CONEY'.

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