Woman showing purpose, the first person to get stuck in (4)
I believe the answer is:
enid
'woman' is the definition.
'purpose the first person to get stuck in' is the wordplay.
'purpose' becomes 'end' (both can mean a goal).
'the first person' becomes 'I' (first-person pronoun).
'to get stuck in' indicates putting letters inside.
'end' placed around 'i' is 'ENID'.
'showing' acts as a link.
(Other definitions for enid that I've seen before include "Dine out on this girl's name also" , "W - - Blyton" , "- Blyton, twentith century writer" , "Geraint's wife's" , "Geraint's loved one" .)