Put inside loose, fall out (7)

I believe the answer is:

dispute

I'm a little stuck... Click here to teach me more about this clue!

'fall out' is the definition.
'dispute' can be an answer for 'fall' (thesaurus). I'm not sure about the 'out' bit.

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for dispute that I've seen before include "Argument, contention" , "conflict" , "Question or deny accuracy or validity" , "Row" , "Altercation" .)

I've seen this clue in the Evening Standard.

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