Very keen intent to dump one pompous girl (5)
I believe the answer is:
madam
'pompous girl' is the definition.
(madam can mean a pompous or bossy girl)
'very keen intent to dump one' is the wordplay.
'very keen' becomes 'mad' (I've seen this in other clues).
'intent' becomes 'aim' (synonyms).
'to dump' is a deletion indicator.
'one' becomes 'i' (Roman numeral).
'aim' with 'i' removed is 'am'.
'mad'+'am'='MADAM'
(Other definitions for madam that I've seen before include "How one may address a woman" , "Term of address to a woman" , "Titled lady" , "Bossy girl" , "Stuck-up girl" .)