Street just containing area without corners (8)
I believe the answer is:
straight
'without corners' is the definition.
(as in a straight road)
'street just containing area' is the wordplay.
'street' becomes 'st' (abbreviation).
'just' becomes 'right' (similar in meaning).
'containing' means one lot of letters goes inside another.
'area' becomes 'a' (maths abbreviation).
'right' going around 'a' is 'raight'.
'st'+'raight'='STRAIGHT'
(Other definitions for straight that I've seen before include "Instantly - honest" , "Honourable" , "not gay" , "Not curved or bent" , "Frank" .)