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Way, way back after English side gets cowboy hat (7)

Ross

I believe the answer is:

stetson

I'm a little stuck... Click here to teach me more about this clue!

'cowboy hat' is the definition.
(I've seen this in another clue)

'way way back after english side' is the wordplay.
I cannot quite understand how this works, but
'way' could be 'st' (abbreviation for street) and 'st' is found within the answer.
'english' could be 'e' (abbreviation as in OED) and 'e' is located in the answer.
'side' could be 'on' (I've seen this in other clues) and 'on' is found within the answer.
'way back' could be 'ts' ('st' abbreviation for street, written backwards) and 'ts' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...

'gets' is the link.

Can you help me to learn more?

(Other definitions for stetson that I've seen before include "Style of hat" , "Hat with wide brim and high crown, maybe a cowboy's" , "Hat with broad brim and high crown" , "Cowboy wear" , "Man's hat with wide brim and high crown" .)

I've seen this clue in the Sydney Morning Herald.
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