Expertise of some teachers sent pedagogy up (9)
I believe the answer is:
adeptness
'expertise' is the definition.
(thesaurus)
'some teachers sent pedagogy up' is the wordplay.
'some' says the answer is hidden in the clue (some of the parts of the word are used).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'ssentpeda' is hidden within 'teachers sent pedagogy'.
'ssentpeda' reversed gives 'ADEPTNESS'.
'of' acts as a link.
(Other definitions for adeptness that I've seen before include "Deftness, adroitness" , "complete skill" .)