I've dealt with this before.

The first thing I want to know is what the employee is actually doing after he finishes the task. Is he standing around? On his phone? Talking to other people? Or is he simply waiting because nobody has told him what comes next?

There's a difference.

It's easy to look at somebody standing around and decide they don't have initiative. But before I make that judgment, I want to know whether I've actually established the expectation.

One thing I've done in the past is very simple:

“When you're finished with this, come find me. I've got something else for you.”

Now I've removed the ambiguity.

He knows that finishing the task doesn't mean he's finished working. His next responsibility is to come find me.

Then I watch what happens.

If he finishes and comes looking for me, maybe I didn't have an initiative problem at all. He may have simply needed direction and a clear expectation.

If he finishes, knows he's supposed to come find me, and instead disappears, gets on his phone, or wastes time until somebody finds him, now I have different information.

That's why I wouldn't immediately make the phone the problem. Taking somebody's phone away might stop one behavior, but it doesn't necessarily correct the underlying issue.

Before I decide someone lacks initiative, I want to make sure I haven't created an environment where waiting for instructions is exactly what I've taught them to do.

Set the expectation first. Then hold them accountable to it.

And there's a natural second stage to this that we shouldn't force into the answer: once the employee consistently comes looking for the next task, then you can start teaching him to recognize what needs to happen next without asking.

That's development. First, you establish responsibility. Then you build judgment.