Sprinted over at some speed to tell story (7)
I believe the answer is:
narrate
'tell story' is the definition.
(a narrator tells a story)
'sprinted over at some speed' is the wordplay.
'sprinted' becomes 'ran' (I've seen this before).
'over' shows that the letters should be reversed in order.
'at' means one lot of letters go next to another.
'some speed' becomes 'rate' (both can mean pace).
'ran' backwards is 'nar'.
'nar'+'rate'='NARRATE'
'to' acts as a link.
(Other definitions for narrate that I've seen before include "Tell the tale." , "Tell us the story" , "Read" , "Give a spoken account" , "Give (film) commentary" .)