Sort of business college once attached to Doctor No (8)
I believe the answer is:
monopoly
'sort of business' is the definition.
(monopoly can mean a dominant business)
'college once attached to doctor no' is the wordplay.
'college once' becomes 'poly' (short for polytechnic, former type of college).
'attached to' says to put letters next to each other.
'doctor' becomes 'mo' (medical officer).
'mo'+'no'='mono'
'poly' after 'mono' is 'MONOPOLY'.
(Other definitions for monopoly that I've seen before include "Board game with property dealing" , "control of market" , "Single-source supply" , "Position of having no competitors" , "Board game or exclusive business possession" .)