6ft fence on 3ft concrete posts

Hi everyone
A neighbour has asked me to do her fence, she wants a tall privacy fence putting up between her and the rental house on the other side, a traditional fence with no gaps. It runs between the house wall and a tall block wall at the back of the garden, with one 3ftconcrete post in the middle. Its about 6m long in total

Is it OK to bolt some timber posts either side of the concrete post, as you would on a lower fence, but sticking up 3ft above the post, and bracing the gap above the concrete? Or would I have to dig down and pull the old post out and put a longer one in. Thanks

If I understand this correctly .
There is a run of 6 metres between 2 walls. There is currently 1 post in the middle ( 3 metres ) ?

If thats it then I would leave the post where it is or just break it off ( and make good ) and instead of having 2 x 3 metre bays of fence I would put in 2 new posts and have 3 x 2 metres bays instead.

You coming of the wall with wall plates / battens ?

Yes thats right, I had a better look today, turns out theres another concrete post about 40mm from the garden wall. but thats pretty much irrelevant

I was hoping to just bolt 3x3 posts to the house wall and the pillar at the end of the garden wall, and fix the fence to thatwanted other opinions before I end up pulling her wall over.

I assume the smaller posts might not go deep enough to put that much stress on it, I dont really have the know-how or tools to put new posts in concrete ground, so I might tell her she'll have to get a pro on it