Lack of interest in a course close to Turnberry (6)
I believe the answer is:
apathy
'lack of interest' is the definition.
'a course close to turnberry' is the wordplay.
'course' becomes 'path' ('path' can be a synonym of 'course').
'close to' suggests the final letters (the close/ending of).
The last letter of 'turnberry' is 'y'.
'a'+'path'+'y'='APATHY'
'in' acts as a link.
(Other definitions for apathy that I've seen before include "Lack of interest or concern" , "Torpor" , "lack of involvement" , "Lack of interest in things in general" , "Lack of emotion and interest" .)