One enters London school after European woman (5)
I believe the answer is:
elsie
'woman' is the definition.
'one enters london school after european' is the wordplay.
'one' becomes 'I' (Roman numeral).
'enters' indicates putting letters inside.
'london school' becomes 'lse' (London School of Economics).
'after' is a charade indicator (letters next to each other).
'european' becomes 'E' (abbreviation e.g. EU).
'i' placed within 'lse' is 'lsie'.
'lsie' put after 'e' is 'ELSIE'.
(Other definitions for elsie that I've seen before include "woman" , "Lady" , "Name for girl" , "Girl's name" , "Female name; rhymes with London football team" .)