Yes but it will be a pain in the bum to dig around a post in situ. It will probably be quicker if you can carefully remove it (you might need to prop the fence) dig a new hole and concrete in.

Mitre 10 has a video:

100% what I would do " dig around it and put concrete down "

First stabilise the post in the correct position with two  pegs and two boards that are perpendicular to each other.  Then dig out add concrete, check/adjust position, leave to set and then refill.

I'm sure M10 or someone has video showing how to do this for new post, that will give you the idea.  Maybe in this vid.

How to Build a Fence | Mitre 10 Easy As DIY - YouTube