Briefly promote theory that’s upset old magistrates (7)

'old magistrates' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'briefly promote theory that's upset' is the wordplay.
'briefly' means to remove the last letter.
'promote' becomes 'sell' (sell can mean to promote or advertise).
'theory' becomes 'idea' (idea can mean a theory).
'that's upset' says the letters should be written backwards.
'sell' with its final letter taken off is 'sel'.
'sel'+'idea'='selidea'
'selidea' in reverse letter order is 'AEDILES'.

Can you help me to learn more?