Magnate not coy in flotation? (6)
I believe the answer is:
Here is my best explanation:
'magnate' is the definition.
('tycoon' can be a synonym of 'magnate')
'not coy in flotation?' is the subsidiary indication.
'in flotation?' indicates anagramming the letters.
'notcoy' is an anagram of 'tycoon'.
(Other definitions for tycoon that I've seen before include "Wealthy magnate", "Rich and powerful businessman", "Wealthy businessman", "Powerful industrialist", "A business magnate or wealthy industrialist", "Big cheese in business", "Rich businessperson", "Wealthy or powerful business person", "Capitalist" and "Captain of industry".)