An odd personality part in the play (9)

I believe the answer is:

character

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This might be a double definition.

'an odd personality' is the first definition.
'character' can be an answer for 'personality' (I've seen this before). I'm not sure about the 'an odd' bit.

'part in the play' is the second definition.
'character' can be an answer for 'part' (synonyms). I'm unsure of the 'in the play' bit.

Can you help me to learn more?

(Other definitions for character that I've seen before include "strength of mind" , "Nonconformist" , "Someone in play" , "card" , "Eccentric person" .)

I've seen this clue in The Irish News.

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