Peer drops out though he did well (9)

I believe the answer is:

prospered

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'did well' is the definition.
(I've seen this in another clue)

'peer drops out' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'peer'+'drops'='peerdrops'
'peerdrops' is an anagram of 'PROSPERED'.

'though he' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for prospered that I've seen before include "proved successful" , "Make steady progress, flourished" , "Succeeded - made good" .)

I've seen this clue in The Globe and Mail.

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