Supervised staff matured (7)
I believe the answer is:
managed
'supervised' is the definition.
('manage' can be a synonym of 'supervise')
'staff matured' is the wordplay.
'staff' becomes 'man' (as in staffing or manning a particular place).
'matured' becomes 'aged' ('age' can be a synonym of 'mature').
'man'+'aged'='MANAGED'
(Other definitions for managed that I've seen before include "Supervised (staff)" , "Contrived" , "Controlled, was in charge of" , "Coped" , "Ran, administered" .)