Roman poet briefly held by groups of old Reds (7)

'old reds' is the definition.
Although both the answer and definition are plural nouns, I cannot see how one could define the other.

'roman poet briefly held by groups' is the wordplay.
'roman poet' becomes 'ovid' (I've seen this before).
'briefly' means to remove the last letter.
'held by' means one lot of letters goes inside another.
'groups' becomes 'sets' (I've seen this in other clues).
'ovid' with its last letter removed is 'ovi'.
'ovi' going within 'sets' is 'SOVIETS'.

'of' is the link.

Can you help me to learn more?