Study centre - expert securing a degree - gosh! (7)
I believe the answer is:
academy
'study centre' is the definition.
'expert securing a degree gosh' is the wordplay.
'expert' becomes 'ace' (ace is a kind of expert).
'securing' is an insertion indicator.
'degree' becomes 'd' (abbreviation for the degree in measuring angles).
'gosh' becomes 'my' (both are old-fashioned expressions of surprise).
'a'+'d'='ad'
'ace' placed around 'ad' is 'acade'.
'acade'+'my'='ACADEMY'
(Other definitions for academy that I've seen before include "Secondary school" , "Grove" , "School for specialised education" , "Specialist school" , "Institution for the advancement of the arts and sciences" .)