Crossword Genius

Go very quietly around Middlesex (3)

Ross

I believe the answer is:

pep

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'go' is the definition.
(I've seen this before)

'very quietly around middlesex' is the wordplay.
'very quietly' becomes 'pp' (musical abbreviation for pianissimo).
'around' means one lot of letters goes inside another.
'middlesex' becomes 'e' (I can't justify this - if you can you should believe this answer much more).
'pp' placed around 'e' is 'PEP'.

Can you help me to learn more?

(Other definitions for pep that I've seen before include "Go" , "Energy, zip" , "Energy, liveliness" , "Energy or enthusiasm" , "Ginger; tax-free investment" .)

I've seen this clue in the Evening Standard.
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