Adding new value to existing Stream

The StreamEx library has corresponding #prepend() and #append() methods. Here's an example how they can be used:

StreamEx.of("second").prepend("first").append("third").forEach(System.out::println);

An output is as follows:

first
second
third

How about

return Stream.concat(stream, Stream.of(elem));

this is assuming the original Stream is finite. If it's not, you can concat them in a reversed order.

The question belies an incorrect assumption: that streams actually contain their data. They do not; streams are not data structures, they are a means for specifying bulk operations across a variety of data sources.

There are combinators for combining two streams into one, such as Stream.concat, and factories for creating streams from a set of known elements (Stream.of) or from collections (Collection.stream). So you can combine these if you want to produce a new stream that is the concatenation of the stream you have in hand, along with a new stream describing the new elements.

The problem in your PECS example is that you've got three occurrences of ? super T, and you are assuming they describe the same type, but they do not. Each occurrence of a wildcard corresponds to a unique capture, which isn't what you want; you need to give that type variable a name so the compiler knows that the type of the list and the type of the input stream are the same. (Also, don't materialize a collection; that's expensive, and potentially non-terminating if the stream is not finite. Just use concat.) So the answer is: you just got the generics wrong. Here's one way to do it:

public<T> Stream<T> appendToStream(Stream<? extends T> stream, T element) {
    return Stream.concat(stream, Stream.of(element));
}

You confused yourself with PECS because you were thinking about "inserting" into the stream, when in fact you're consuming from it.