Teach girl badly, being exceptionally drowsy (9)
I believe the answer is:
lethargic
'exceptionally drowsy' is the definition.
'teach girl badly' is the wordplay.
'badly' is an anagram indicator.
'teach'+'girl'='teachgirl'
'teachgirl' is an anagram of 'LETHARGIC'.
'being' is the link.
(Other definitions for lethargic that I've seen before include "The garlic (anag.)" , "Sluggish and apathetic" , "Unenergetic" , "Lacking in energy or vitality" , "without energy" .)