Dodgy period behind the scenes (8)
I believe the answer is:
offstage
'behind the scenes' is the definition.
('offstage' can be a synonym of 'behind the scenes')
'dodgy period' is the wordplay.
'dodgy' becomes 'off'.
'period' becomes 'stage' (e.g. a stage in history**).
'off'+'stage'='OFFSTAGE'
(Other definitions for offstage that I've seen before include "Not visible to the audience" , "out of sight of house" , "out of sight of the audience" , "Behind-the-scenes" , "From the wings of a theatre?" .)