LINQ new instance when SingleOrDefault returns null

You could use DefaultIfEmpty and use that instance as default value:

return _addresses.Where(x => x.TypeId == AddressType.Delivery)
                 .DefaultIfEmpty(new Adress())
                 .Single();

You could create your own extension method, like this:

public static T NewIfNull<T>(this T obj) where T: class, new()
{
   return obj ?? new T();
}

... then tack a usage onto the end of SingleOrDefault:

var singleResult = myCollection.SingleOrDefault().NewIfNull();

... or because the logic is so simple, just inline it as other answers have said.

Instead of

return _addresses.SingleOrDefault(x => x.TypeId == AddressType.Delivery);

Do something like this:

var address = _addresses.SingleOrDefault(x => x.TypeId == AddressType.Delivery);

if(address == null)
    address = new Address();

return address;

Use the null-coalescing operator:

return _addresses
    .SingleOrDefault(x => x.TypeId == AddressType.Delivery) ?? new Address();

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The expression

x ?? y

yields x if x is not null, otherwise y. You can chain the operator

x ?? y ?? z ?? t

This returns the first non-null value or null if all of them are null.

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UPDATE

Note that SingleOrDefault throws an exception if the sequence has more than one element. If you need the first element of a sequence possibly having no or more than one element, use FirstOrDefault instead.