The Pentagon, perhaps, or the post office on Lygon Street (7)
I believe the answer is:
polygon
'the pentagon perhaps' is the definition.
(pentagon is a kind of polygon)
'on lygon street' is the wordplay.
'on' means one lot of letters go next to another.
'street' becomes 'po' (I can't justify this - if you can you should believe this answer much more).
'lygon' put after 'po' is 'POLYGON'.
'or the post office' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for polygon that I've seen before include "shape" , "Figure with many sides" , "Many-sided plane figure" , "Geometric figure with five or more sides" , "Closed plane figure with three or more straight sides" .)