Lack of interest in a course beginning in York (6)
I believe the answer is:
apathy
'lack of interest' is the definition.
(I've seen this before)
'a course beginning in york' is the wordplay.
'course' becomes 'path' (path can mean a route or course).
'beginning in york' becomes 'y' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'a'+'path'+'y'='APATHY'
'in' is the link.
(Other definitions for apathy that I've seen before include "Absense of interest or emotion" , "Absence of emotion or enthusiasm" , "Indifference - listlessness" , "Torpor" , "Complete lack of interest, indifference" .)