What some do to the wheel? Check where the air goes (8)

I believe the answer is:
reinvent
'what some do to the wheel?' is the definition.
The definition suggests a singular noun but the answer is not.
'check where the air goes' is the wordplay.
I cannot really understand how this works, but
'check' could be 'rein' (both can mean to control or limit) and 'rein' is located in the answer.
'air' could be 'vent' (both can mean to express or reveal) and 'vent' is located in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for reinvent that I've seen before include "Change (something) so as to appear entirely new" , "Coin not necessarily found" , "Recreate" , "design again" , "Change (something) so much as to appear new" .)
