A source of inspiration going around some chariot arena (5)
I believe the answer is:
erato
'a source of inspiration' is the definition.
(one of the muses in Greek myth)
'going around some chariot arena' is the wordplay.
'going around' shows that the letters should be reversed in order.
'some' says the answer is hidden in the clue (some of the parts of the word are used).
'otare' is hidden in the letters of 'chariot arena'.
'otare' in reverse letter order is 'ERATO'.
(Other definitions for erato that I've seen before include "Muse of lyric love-poetry" , "poetic patroness" , "Muse of 11 and 23" , "Muse of lyric poetry and mime" , "One inspiring" .)