Into test-playing again, in a way (6)
I believe the answer is:
'a way' is the definition.
(street is a kind of way)
'into test-playing again' is the wordplay.
'into' means one lot of letters goes inside another.
'playing' indicates anagramming the letters.
'again' becomes 're'.
'test' is an anagram of 'stet'.
'stet' going around 're' is 'STREET'.
'in' is the link.
(Other definitions for street that I've seen before include "Part of motorist's route", "lane", "Urban thoroughfare", "See 7", "Tester in public road".)