I’d get the old concrete out first before working out a solution, had to replace an old fence last year and they’d used a bag of postcrete on one, then two bags (or more) on the next, i broke one up and it left a massive hole, which required work before putting a new post in. My guess would be they did similar to just removing old postcrete, then filling the hole without narrowing it back.
After that though, as above, prep the hole to protect against water ingress, then put post in and add more postcrete, i tend to mix it in a bucket and the pour, just makes a better cement, also making sure to secure post for the 30 minutes or so to set, i.e. that it’s at the right angle and rotation for the fence.