Skip lessons given by her? (4)
I believe the answer is:
miss
This clue is a double definition.
'skip' is the first definition.
(thesaurus)
'lessons given by her?' is the second definition.
(female teachers are referred to as Miss)
(Other definitions for miss that I've seen before include "Overlook - misfire - young lady" , "Suffer from the lack of" , "Don't hit" , "Fail to notice; avoid" , "Fail to reach" .)