Society girl in Underground, sent up to visit poet (9)
I believe the answer is:
debutante
'society girl' is the definition.
(girl debuting in upper-class, fashionable society)
'underground sent up to visit poet' is the wordplay.
'underground' becomes 'tube' (the London Underground is nicknamed the Tube).
'sent up' shows that the letters should be reversed in order.
'to visit' indicates putting letters inside.
'poet' becomes 'Dante' (Dante is an example).
'tube' backwards is 'ebut'.
'ebut' inserted inside 'dante' is 'DEBUTANTE'.
'in' acts as a link.
(Other definitions for debutante that I've seen before include "young lady coming out" , "eligible young lady?" , "Young lady making her first appearance in society" , "Society girl" , "one about to come out" .)