Hunch in shed giving lessons (7)
I believe the answer is:
tuition
'lessons' is the definition.
(I've seen this before)
'hunch in shed' is the wordplay.
'hunch' becomes 'intuition' (synonyms).
'shed' indicates named letters should be taken away ('shed' as in 'cut away').
'intuition' with 'in' removed is 'TUITION'.
'giving' is the link.
(Other definitions for tuition that I've seen before include "(Individual) instruction" , "Personal coaching" , "Teaching, instruction" , "Training" , "Schooling" .)