Award given for small part (6)
I believe the answer is:
degree
This clue is a double definition.
'award' is the first definition.
(I know that degree is a type of award)
'for small part' is the second definition.
(I've seen this before)
'given' is the link.
(Other definitions for degree that I've seen before include "Position on a scale" , "Unit of measurement of angles" , "It's given to college graduates" , "Angular unit and college award" , "Award given to a college graduate" .)