Period of history, period enthralling one (5,3)
I believe the answer is:
stone age
'period of history' is the definition.
'period enthralling one' is the wordplay.
'period' becomes 'stage' (e.g. a stage in history).
'enthralling' is an insertion indicator.
'stage' placed around 'one' is 'STONE-AGE'.
(Other definitions for stone age that I've seen before include "Early epoch when man used pre-metal tools" , "Early period" , "Pre-historic era" , "Neolithic" , "before copper came in" .)