... with character Mike is succeeding, large Eddy (4)

I believe the answer is:

well

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'mike is succeeding large eddy' is the definition.
I can't judge whether this defines the answer.

'with character' is the wordplay.
'with' becomes 'w' (abbreviation).
'character' becomes 'ell' (ell is a kind of character).
'w'+'ell'='WELL'

Can you help me to learn more?

(Other definitions for well that I've seen before include "Profoundly" , "run" , "Fortunate" , "Pour - thoroughly" , "Healthy - water supply" .)

I've seen this clue in The Telegraph.

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