That looks like a royal PITA...
If it was me: Drill/Dig out the old post then assess the situation (how deep etc.). Use a shop vac to get the hole really clean. The post probably extends below the concrete into the dirt.
So what are you going to replace the post with? I'd use a galvanized steel box tube. Cut a hole large enough for new concrete in the existing the concrete (using a wet saw and chisel). You should be able to level the new concrete off so it blends well.
10 odd years ago I built a small garage. This is how I secured the posts.
Note you don't need a massive hole but it has to be deep. Deeper than the bottom on the new posts.
