Quite open managing directors? (10)

I believe the answer is:

aboveboard

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'quite open' is the definition.
'aboveboard' can be an answer for 'open' (similar in meaning). I'm not certain of the 'quite' bit.

'managing directors?' is the wordplay.
'managing' becomes 'above' (I can't explain this - if you can you should believe this answer much more).
'directors?' becomes 'board' (board of directors).
'above'+'board'='ABOVEBOARD'

Can you help me to learn more?

I've seen this clue in The Irish News.

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