ideas to remove broken fence post?

I'm likely a day late and a dollar short cuz you have likely fixed it by now but I fixed a buddy's post very similar to your situation. I drilled out the center as much as possible. It was roughly a foot down to the existing old post. I used a " post spike" and drove it down in the hole ( using the cut off from the new post) into the old post just before the bottom square part was 2 inches above the concrete. I mixed up some concrete and poured it around and down into the hole. I attached the new post and drove it down below the level of the driveway another inch and used a little more concrete to level off around the post. A day later I attached the gate. It has held up well.

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