Hunch in shed, giving instruction (7)
I believe the answer is:
'instruction' is the definition.
(tuition is a kind of instruction)
'hunch in shed' is the wordplay.
'hunch' becomes 'intuition' ('intuition' can be a synonym of 'hunch').
'shed' suggests deleting specific letters ('shed' as in 'cut away').
'intuition' with 'in' taken away is 'TUITION'.
'giving' acts as a link.
(Other definitions for tuition that I've seen before include "practice" , "Schooling" , "Teaching, instruction" , "Personal coaching" , "Lessons" .)