Schoolgirl and I on an assignment (7)
I believe the answer is:
mission
'an assignment' is the definition.
(mission is a kind of assignment)
'schoolgirl and i on' is the wordplay.
'schoolgirl' becomes 'miss' (I've seen this before).
'and' is a charade indicator (letters next to each other).
'miss'+'i'+'on'='MISSION'
(Other definitions for mission that I've seen before include "Task assigned to be done" , "Assignment; expedition" , "Important assignment" , "Special assignment" , "In religious campaign" .)