College administrator skinned bear (4)
I believe the answer is:
ursa
'bear' is the definition.
(Latin name for bear as in Ursa Major)
'college administrator skinned' is the wordplay.
'college administrator' becomes 'bursar' (someone who manages a college's finances).
'skinned' says to take the centre.
The middle of 'bursar' is 'URSA'.
(Other definitions for ursa that I've seen before include "Bear (constellation)" , "Major and Minor, the Bear constellations" , "and 18 Down: The Great Bear" , "'Major and Minor, constellations (4)'" , "(& 19 across) Plough constellation" .)