Ingrid is going round on horseback (6)
I believe the answer is:
riding
'on horseback' is the definition.
(I've seen this before)
'ingrid is going round' is the wordplay.
'is going round' indicates anagramming the letters.
'ingrid' is an anagram of 'RIDING'.
(Other definitions for riding that I've seen before include "Establishment teaching horsemanship" , "Travelling on horseback" , "being carried" , "Parliamentary constituency (Canada) - former administrative district (Yorkshire)" , "Division of Yorkshire" .)