The “red” kind backs out of the way (4)
I believe the answer is:
deer
'the red kind' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.
'backs out of the way' is the wordplay.
'backs' becomes 'der' (I can't justify this - if you can you should give a lot more credence to this answer).
'out of' indicates putting letters inside.
'the way' becomes 'e' (Compass direction - East).
'der' going around 'e' is 'DEER'.
Can you help me to learn more?
(Other definitions for deer that I've seen before include "does for example" , "Bucks and does?" , "Antlered animal" , "Hoofed grazing animal" , "The - Hunter, 1978 film" .)