You need to age venison for 7 days minimum. Should ideally be slightly chilled, too.
You can buy game fridges/chillers or buy kits which convert entire rooms into chilled larders. One of the small hunting estates near to where I live use a converted shipping container.
A common thing to do here in Scotland is to buy commercial drink chillers or large milk chillers (the type used in coffee shops), or even domestic larder fridges if you're only hunting small species like roe, or even birds like pigeon, and convert them into mini larders. You can buy these used for very cheap on ebay etc. Again, you can buy kits which increase airflow, reduce humidity etc. Pic related.
There are some guides to doing this on
deerstalkingdirectory.co.uk 