Rejected new street map that's variable and eccentric (4)
I believe the answer is:
zany
'eccentric' is the definition.
(I've seen this before)
'rejected new street map that's variable' is the wordplay.
'rejected' says the letters should be written in reverse.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'street map' becomes 'A-Z' (an 'A to Z' is a street map).
'that's variable' becomes 'y' (algebra).
'n'+'az'='naz'
'naz' backwards is 'zan'.
'zan'+'y'='ZANY'
'and' acts as a link.
(Other definitions for zany that I've seen before include "Endearingly funny" , "Screwball" , "Amusingly idiosyncratic" , "Left-field - foolish" , "Mad" .)