Teaching and feeling not hot (7)
I believe the answer is:
tuition
'teaching' is the definition.
(I know that tuition is a type of teaching)
'feeling not hot' is the wordplay.
'feeling' becomes 'intuition' (intuition is a kind of feeling).
'not' is a deletion indicator.
'hot' becomes 'in' (both can mean fashionable).
'intuition' with 'in' taken out is 'TUITION'.
'and' acts as a link.
(Other definitions for tuition that I've seen before include "Personal coaching" , "practice" , "Training" , "Schooling" , "Teaching, instruction" .)