Bowl and a new period's over (5)
I believe the answer is:
arena
'bowl' is the definition.
('arena' can be a synonym of 'bowl')
'a new period's over' is the wordplay.
'a new' becomes 'an' (I've seen this in other clues).
'period' becomes 'era' (era is a kind of period**).
'over' shows that the letters should be reversed in order.
'an'+'era'='anera'
'anera' back-to-front is 'ARENA'.
'and' acts as a link.
(Other definitions for arena that I've seen before include "battlefieId" , "The place of action" , "Playing field or boxing ring" , "Ring for contest" , "sports ground" .)