She's very keen to get a stage part (5)
I believe the answer is:
madge
'she's' is the definition.
'keen to get a stage part' is the wordplay.
'keen' becomes 'mad' (both can mean enthusiastic about).
'to get a stage part' becomes 'ge' (I can't explain this - if you can you should give a lot more credence to this answer).
'mad'+'ge'='MADGE'
'very' is the link.
Can you help me to learn more?
(Other definitions for madge that I've seen before include "Madonna's nickname" , "girl" .)