Former PM progressed embracing right (7)

I believe the answer is:

cameron

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'former pm' is the definition.
'cameron' can be an answer for 'pm' (David Cameron, former UK prime minister). I'm not certain of the 'former' bit.

'progressed embracing right' is the wordplay.
'progressed' becomes 'came on' ('come on' can be a synonym of 'progress').
'embracing' means one lot of letters goes inside another.
'right' becomes 'r' (common abbreviation).
'cameon' placed around 'r' is 'CAMERON'.

Can you help me to learn more?

(Other definitions for cameron that I've seen before include "Clan member" , "Romance (anag) - party leader" , "David --, PM" , "Conservative leader" , "GB PM" .)

I've seen this clue in The Telegraph.

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