Years ago, it wasn't uncommon to hang beef or Red deer (elks smaller cousin) for up to 6 weeks..

These days for our smaller deer most hang for 7 to 14 days depending on temps.

I like to hang in the skin for for say 10 days at just above freezing ( I have a small meat fridge)..I then skin the day before I intend to butcher to allow the meat a final 24 hours to "firm up"..