Former American president supports Greek to calm oil producer (10)

I believe the answer is:

greasebush

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'calm oil producer' is the definition.
I know nothing about this answer so I can't tell whether this works.

'former american president supports greek' is the wordplay.
'former american' becomes 'ease' (I can't explain this - if you can you should give a lot more credence to this answer).
'president' becomes 'bush' (George H W Bush or George W Bush).
'supports' says to put letters next to each other (bottom letters provide a support for the top ones).
'greek' becomes 'gr' (abbreviation for Greek).
'ease'+'bush'='easebush'
'easebush' after 'gr' is 'GREASEBUSH'.

'to' acts as a link.

Can you help me to learn more?

I've seen this clue in The Independent.

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