Crossword Genius

Publicity bod hurried round about and was successful (9)

Ross

I believe the answer is:

prospered

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'publicity bod hurried round about and was successful' is the definition.
I can't tell whether this definition defines the answer.

'hurried round about and was successful' is the wordplay.
'hurried' becomes 'sped' ('speed' can be a synonym of 'hurry').
'round' indicates putting letters inside.
'about' becomes 're' ('re' means regarding or about).
'and' means one lot of letters go next to another.
'was successful' becomes 'pro' (I can't explain this - if you can you should give a lot more credence to this answer).
'sped' enclosing 're' is 'spered'.
'spered' after 'pro' is 'PROSPERED'.

Can you help me to learn more?

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

I've seen this clue in The Times.
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