Girl employed in teaching riding (6)
I believe the answer is:
ingrid
'girl' is the definition.
'employed in teaching riding' is the wordplay.
'employed in' says the answer is hidden in the clue.
'INGRID' is hidden within 'teaching riding'.
(Other definitions for ingrid that I've seen before include "Riding (anag) - girl's name" , "girl" , "___ Bergman, Swedish actress" , "A lady" .)