Second refusal by old college to provide game (8)
I believe the answer is:
monopoly
'game' is the definition.
(Monopoly is an example)
'second refusal by old college' is the wordplay.
'second' becomes 'mo' (both are short periods of time).
'refusal' becomes 'no'.
'by' means one lot of letters go next to another.
'old college' becomes 'poly' (polytechnic).
'mo'+'no'+'poly'='MONOPOLY'
'to provide' acts as a link.
(Other definitions for monopoly that I've seen before include "Situation of one company's dominance in a particular market" , "Position of having no competitors" , "Sole seller" , "Market in which there are many buyers but only one seller" , "Exclusive control - board game" .)