Tea in the movies, it keeps things moving (5-5)

I believe the answer is:

drive-chain

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'it keeps things moving' is the definition.
I don't know anything about this answer so I cannot judge whether this works.

'tea in the movies' is the wordplay.
'tea' becomes 'chai' (I've seen this before).
'in the' indicates putting letters inside.
'movies' becomes 'driven' (I can't explain this - if you can you should believe this answer much more).
'chai' going into 'driven' is 'DRIVE-CHAIN'.

Can you help me to learn more?

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

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