What are you after Barry? - options or whats required to replace the post.
Is the post solid below the top rail. If so, maybe a cosmetic repair to cut the top off and fix/re-fit another in its place as a short term solution. Use dowel or maybe biscuits to hold it in place, glue, sand, paint and it would probably look OK for the sale...no one will notice
If not, and the post is rotted out then pull the post and replace. Not going to be an easy job.
The unknown is how big is the lump of concrete holding the post in the ground...given its got a gate hanging off it, could be a decent size which will dictate if its possible to do a minimum dismantle
Cut the concrete at the base in front of the post, pull the bricks (are they laid on concrete?), detach the rails - pull them back out of the way, detach the rear support but leave in place and detach gate.
Whats the plinth board attached to? Can it be pulled forward?
How deep is the concrete garden edging behind the post? can it be removed or does it need to be cut/broken up or can it be left in place depending on what you find in the next step
Depending on what you find with the lump of concrete holding in the post, you might be able to take a bit more out in front and bricks to the side, then jack hammer the concrete around the post to break it up without removing the thick concrete garden edging behind.
If that works, should be easy to clear the hole, set up the new post with rail cut outs plumb and concrete into place. Put everything back together.
Good luck!