Not quite a shining unit of circular measure (6)
I believe the answer is:
radian
'unit of circular measure' is the definition.
'radian' can be an answer for 'measure' (radian is a kind of measure). I am not certain of the 'unit of circular' bit.
'not quite a shining' is the wordplay.
'not quite' means to remove the last letter.
'a shining' becomes 'radiant' (I've seen this in another clue).
'radiant' with its last letter taken off is 'RADIAN'.
Can you help me to learn more?
(Other definitions for radian that I've seen before include "SI unit of plane angle" , "A mathematical unit" , "Angle of approx. fifty seven degrees" , "Unit in the maths department" , "Unit of angular measure" .)