If properly chilled after capture and carefully stored in the fridge, fish fillets will last for up to a week. The key to a long shelf life is to clean and dry the fish well before storage and to keep it dry in the fridge.
Wipe the fillets down with a paper towel, removing any blood and slime. Don’t wash the fish in freshwater – it will only make the fillets deteriorate more quickly. Freshwater is drawn into the saltier flesh by osmosis, softening the fillets and turning them mushy. Washing in seawater’s OK, but dry the fillets well before refrigerating.
Once in the fridge, don’t let fish fillets soak in their own juices. Moisture will naturally leach out of the fillets and can quickly spoil any fish allowed to bathe in it. Lay fillets on a rack so that any juices can drain into the container below. And ensure there is adequate airflow around the fillets – a large container is better than a small one and you should never wrap fish tightly in plastic film. Plain paper towels work well, but must be replaced every day or so.
It’s always better to store fish in a single layer, but if you have a lot of fillets to store you can stack them with a paper towels between each fillet. Remember to replace the paper every day or so. One easy option, seen in restaurant kitchens, is to place the fillets on at upturned plate inside a larger plate, the whole covered with paper towels. The juices drain into the larger plate and fish is able to breathe.
For larger quantities and convenient storage, cheap click-clack-style plastic boxes with racks are readily available from retail outlets selling plastic storage boxes and kitchenware, or you can place a metal or plastic rack inside any ceramic or plastic dish/container. Lay the fish on the rack and close the lid. It should stay in good condition for at least five days, perhaps longer.