How to greet the Queen in shady part of garden? (5)

I believe the answer is:

bower

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'queen in shady part of garden?' is the definition.
'bower' can be an answer for 'queen' (thesaurus). I am not sure about the 'in shady part of garden?' bit.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for bower that I've seen before include "Leafy recess" , "One who shows respect" , "greenery?" , "shady area" , "Garden space shaded from the sun by plants" .)

I've seen this clue in The Guardian.

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