Custard will last for up to 3 days in the fridge before it goes bad.
You should eat the Custard within 3 days of refrigerating it or if not throw it out if the custard has been in the refrigerator longer than 3 days because it could have grown bacteria on it and could make you sick.
If the custard has a bad smell to it or has any mold on the custard then throw it out because that means it's bad.
If it has no bad smell to the custard or has no mold on it then you could taste the custard and if it tastes okay then it probably is okay.
If the custard has a bad taste to it then it's bad and should be thrown out.
All foods that you refrigerate especially things such as custard or any meat foods should not be kept in the refrigerator longer than 3 to 4 days because they can go bad.
Custard can be frozen but just be aware that custard does not freeze well and when frozen the custard has a tendency to separate.
But you can freeze it to make it last longer but I would recommend eating the custard within 3 days and just refrigerate it.