Even on TL 4 or TL 3 or even lower worlds there will be plenty of solutions shipped in from off world, that can be operated at lowers TLs.Well, no, but there's not many TL4 spacecraft, either, so that technique wouldn't be needed. But on TL5+ ships, normal refrigeration ought to be completely doable.
The Icy Ball refrigerator for example, as long as they can build a fire they can make ice.