In the middle of the road, there’s an outer part! (4)
I believe the answer is:
rind
'part' is the definition.
(rind is a kind of part)
'in the middle of the road there's an outer' is the wordplay.
'in the' indicates putting letters inside.
'middle of the road' becomes 'rd' (I can't justify this - if you can you should believe this answer much more).
'there' becomes 'inthatlocation' ('in that location' can be a synonym of 'there').
'an outer' says to hollow out the word (remove centre letters).
'inthatlocation' with its centre taken out is 'in'.
'rd' enclosing 'in' is 'RIND'.
Can you help me to learn more?
(Other definitions for rind that I've seen before include "Skin of orange or melon" , "Outer layer (of cheese)" , "Hard outer skin, of an orange say" , "Peel of an orange" , "Skin of bacon" .)