"The Globe" is turned, first, into a restaurant (6)
I believe the answer is:
bistro
'a restaurant' is the definition.
(I know that bistro is a type of restaurant)
'the globe is turned first into' is the wordplay.
'the globe' becomes 'orb' (synonyms).
'is turned' says the letters should be written backwards.
'first' becomes 'ist' (ist resembles ost).
'into' means one lot of letters goes inside another.
'orb' written backwards gives 'bro'.
'bro' enclosing 'ist' is 'BISTRO'.
(Other definitions for bistro that I've seen before include "somewhere to eat" , "Small informal French cafi" , "Small inexpensive eatery" , "Intimate eatery" , "Modest restaurant" .)