Period covered by champion US historian (9)
I believe the answer is:
herodotus
'historian' is the definition.
(Greek historian)
'period covered by champion us' is the wordplay.
'period' becomes 'dot' (as in a full stop).
'covered by' means one lot of letters go next to another (on top of in a down clue).
'champion' becomes 'hero' (synonyms).
'dot' put after 'hero' is 'herodot'.
'herodot'+'us'='HERODOTUS'
(Other definitions for herodotus that I've seen before include "Ancient Greek historian" , "Famous Greek" , "Historical pioneer" , "Old Greek" .)