Elm Generator Int -> List Int

You cannot get a random list out of Generator because Elm functions are always pure. The only possibility to get a list is to use a command.

A command is a way to tell Elm runtime to do some impure operation. In your case, you can tell it to generate a random list of integers. Then it will return back the result of that operation as an argument of the update function.

To send Elm runtime a command to generate a random value, you can use the function Random.generate:

generate : (a -> msg) -> Generator a -> Cmd msg

You already have Generator a (your intList), so you need to provide a function a -> msg. This function should wrap a (List Int in your case) into a message.

The final code should be something like that:

type Msg =
    RandomListMsg (List Int)
  | ... other types of messages here

update : Msg -> Model -> ( Model, Cmd Msg )
update msg model = case msg of
    ... -> ( model, Random.generate RandomListMsg intList)
    RandomListMsg yourRandomList -> ...

If you don't know about messages and models yet, you should probably get acquainted with the Elm architecture first.

You can provide your own seed value to Random.step, which will return a tuple containing a list and the next seed value. This retains purity because you will always get the same result when you pass the same seed.

Random.step intList (Random.initialSeed 123)
    |> Tuple.first

-- will always yield [69,0,6,93,2]

The answer given by @ZhekaKozlov is typically how you generate random values in an application, but it uses Random.step under the hood with the current time used as the initial seed.