Relocate to protect independent American cinema (5,5)

I believe the answer is:

movie house

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'cinema' is the definition.
(I know that cinema can be written as movie house)

'relocate to protect independent american' is the wordplay.
'relocate' becomes 'move' (I've seen this in another clue).
'to protect' indicates putting letters inside (inserted letters are protected or taken in).
'independent' becomes 'i'.
'american' becomes 'house' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'move' going around 'i' is 'movie'.
'movie'+'house'='MOVIE HOUSE'

Can you help me to learn more?

I've seen this clue in The Guardian.

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