Greek establishment's near broke after tax is misdirected (7)
I believe the answer is:
taverna
'greek establishment's' is the definition.
'near broke after tax is misdirected' is the wordplay.
'broke' indicates anagramming the letters.
'after' is a charade indicator (letters next to each other).
'tax' becomes 'vat' (British sales tax).
'is misdirected' is a reversal indicator.
'vat' written backwards gives 'tav'.
'near' with letters rearranged gives 'erna'.
'erna' after 'tav' is 'TAVERNA'.
(Other definitions for taverna that I've seen before include "Greek bar/restaurant" , "Greek guesthouse" , "pub" , "Small Greek restaurant with bar" , "Greek inn" .)