Inclination of duke that is seen in funds for student (8)
I believe the answer is:
gradient
'inclination' is the definition.
(a tilted or angled slope)
'duke that is seen in funds for student' is the wordplay.
'duke' becomes 'd' (abbreviation).
'that is' becomes 'i.e.' (synonyms).
'seen in' is an insertion indicator.
'funds for student' becomes 'grant' (as in a student grant).
'd'+'ie'='die'
'die' put inside 'grant' is 'GRADIENT'.
'of' is the link.
(Other definitions for gradient that I've seen before include "Bank" , "Angle of slope" , "Level of steepness" , "Degree of slope in a road" , "Third OT book" .)