A proud walk in support of something (5)

I believe the answer is:

strut

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'a proud walk' is the definition.
'strut' can be an answer for 'walk' (strut is a kind of walk). I am not certain of the 'a proud' bit.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for strut that I've seen before include "Support - pompous walk" , "Rigid support" , "Display arrogance" , "Stiffening bar" , "Swagger; bracing bar" .)

I've seen this clue in the Evening Standard.

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