Organisation offered to enlist American behind European fair (9)

I believe the answer is:

unbiassed

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'fair' is the definition.
(similar in meaning)

'organisation offered to enlist american behind' is the wordplay.
'organisation' becomes 'UN' (UN is an example).
'offered to' says to put letters next to each other.
'enlist american behind' becomes 'biassed' (I can't explain this - if you can you should believe this answer much more).
'un'+'biassed'='UNBIASSED'

'european' is the link.
This may not be correct. It may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for unbiassed that I've seen before include "Impartial" , "10 [INDEPENDENT]" .)

I've seen this clue in The Independent.

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