European left Yankee union for the stage (6)
I believe the answer is:
equity
'union for the stage' is the definition.
(UK acting union)
'european left yankee' is the wordplay.
'european' becomes 'E' (abbreviation e.g. EU).
'left' becomes 'quit' (I've seen this before).
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
'e'+'quit'+'y'='EQUITY'
(Other definitions for equity that I've seen before include "Fairness for actors' trade union" , "Moral justice for the actor's union" , "Stake in business" , "Fairness; shareholding" , "Value of a property less debt" .)