Miss equipment returned by lecturer (4)
I believe the answer is:
girl
'miss' is the definition.
('girl' can be a synonym of 'miss')
'equipment returned by lecturer' is the wordplay.
'equipment' becomes 'rig' (rig is a kind of equipment).
'returned' says the letters should be written backwards.
'by' means one lot of letters go next to another.
'lecturer' becomes 'l'.
'rig' reversed gives 'gir'.
'gir'+'l'='GIRL'
(Other definitions for girl that I've seen before include "See 5" , "A young female" , "Maidservant" , "Miss" , "Lassie" .)