Most familiar end street (7)
I believe the answer is:
closest
'most familiar' is the definition.
('close' can be similar in meaning to 'familiar')
'end street' is the wordplay.
'end' becomes 'close' (close can mean the closing part of something).
'street' becomes 'st' (abbreviation).
'close'+'st'='CLOSEST'
(Other definitions for closest that I've seen before include "Nearest or most sultry" , "Nearest or meanest" , "Most intimate" , "Superlatively dense" , "Most stuffy" .)