Art gallery included by staff having moved round (7)

I believe the answer is:

rotated

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'moved round' is the definition.
The definition and answer can be both related to change as well as being past participle verbs.
Maybe there's a link between them I don't understand?

'art gallery included by staff' is the wordplay.
'art gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'included by' is an insertion indicator.
'staff' becomes 'rod' (both can mean a stick or cane).
'tate' inserted inside 'rod' is 'ROTATED'.

'having' is the link.

Can you help me to learn more?

(Other definitions for rotated that I've seen before include "Went round" , "Turned round" , "Spun" , "Turner did?" , "Turned in a circle around an axis" .)

I've seen this clue in The Daily Express.

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