In the warm weather i process right away . I'll debone the whole animal and get it in the fridge or on ice . then you can age as is or package the next time you have time.
I don't notice any bad flavors or lack of tender because i process right away, i do trim the fat and silver skin more than most butchers do though.
If this isn't possible and you need to bring to a butcher the nxt day. put it in a cooler or pack with ice to get the temp down. I have also froze bootles of water to stck in the cavity when i am going to be a while before i get it home .
It wood be great to have my own meat locker but i haven't got around to making one of those, plus my wife won't like that idea. she has to many other projects for me