Democrat moving in to make changes for promoters (5)

I believe the answer is:

admen

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

'for promoters' is the definition.

'democrat moving in' is the wordplay.
'democrat' becomes 'd'.
'moving' becomes 'amen' (I can't explain this - if you can you should believe this answer much more).
'in' indicates putting letters inside.
'd' going within 'amen' is 'ADMEN'.

'to make changes' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

I've seen this clue in The Guardian.

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