Moved fast, exercising in South Dakota (4)
I believe the answer is:
sped
'moved fast' is the definition.
(I've seen this before)
'exercising in south dakota' is the wordplay.
'exercising' becomes 'pe' (abbreviation for Physical Education).
'in' indicates putting letters inside.
'south dakota' becomes 'sd' (abbreviation).
'pe' put into 'sd' is 'SPED'.
(Other definitions for sped that I've seen before include "Moved quickly" , "Rushed" , "Travelled quickly" , "Moved fast" , "Went quickly" .)