First to enter brother's restaurant (6)
I believe the answer is:
bistro
'restaurant' is the definition.
(bistro is a kind of restaurant)
'first to enter brother's' is the wordplay.
'first to' becomes 'ist' (I've seen this in other clues).
'enter' is an insertion indicator.
'brother' becomes 'bro' (short for brother).
'ist' going inside 'bro' is 'BISTRO'.
(Other definitions for bistro that I've seen before include "Small informal french-style resturaunt" , "somewhere to eat" , "Cheap restaurant" , "Small French bar and restaurant" , "Modest restaurant" .)