Royal initially touched on American university (9)
I believe the answer is:
princeton
'american university' is the definition.
(I've seen this before)
'royal initially touched on' is the wordplay.
'royal' becomes 'prince' (prince is a kind of royal).
'initially' indicates taking the first letters.
The initial letter of 'touched' is 't'.
'prince'+'t'+'on'='PRINCETON'
(Other definitions for princeton that I've seen before include "US ivy league university" , "American university" , "where War of Independence battle was fought?" , "Member of the 11 in New Jersey" , "College" .)