Hurried back at speed to provide chronicle (7)
I believe the answer is:
narrate
'chronicle' is the definition.
(thesaurus)
'hurried back at speed' is the wordplay.
'hurried' becomes 'ran' (running is a kind of hurrying).
'back' shows that the letters should be reversed in order.
'at' says to put letters next to each other.
'speed' becomes 'rate' (rate is a kind of speed**).
'ran' backwards is 'nar'.
'nar'+'rate'='NARRATE'
'to provide' acts as a link.
(Other definitions for narrate that I've seen before include "Relate, recount" , "Give (film) commentary" , "Give a spoken account" , "Tell story,recount" , "Relate events" .)