Putting up new fence panels in your garden is no easy task; you first have to check who owns the fence you’re taking down, as in the land the fence is on, or the land the new fence is to be built on. The land could belong to you or your neighbour; if the land belongs to your neighbour, it is generally their responsibility to put a new one up, or if there is no fence, then you can put one up on the boundaries of the land on your side.
If the boundary line for the fence is on your side then it’s ok to put up the new fence; you may have to take down the old fence if one existed, and if one did exists previously, you need to check whether the old posts are concrete metal, or wood, and ascertain whether they can still be used with your new fence.
With wooden posts, the wood may be rotten and the remnants of the fence posts will need to be dug up, and then removed; if not rotten, it might still be best to take them up anyway.
With metal posts, the metal may have become twisted and warped, or even rusty and would have been fixed into place with a concrete base; they will be difficult to remove, but with a bit of smashing, digging and jiggling you can get them out.
With concrete posts, they are most likely going to be in good shape, and may still be usable if the fence panels are for a shorter fence which can be seen over. If you’re looking to build a higher fence, and thinner panels, you won’t be able to fix the panels to the posts and they will need to be removed; the way to get them out of the ground is similar to how you get the metal posts out, but it will require two people to do this and carry the posts away safely, as they can be quite heavy to lift.
Alternatively if the posts are half way on the neighbours side of the land, and they don’t mind, you can get away with leaving the concrete posts where they are, and then drilling three holes into each of them and using coach bolts to fix wooden posts against them, that are flush to the ground; the problem with this is that you have to check whether the old post fence line is level and straight with the garden, otherwise you’re going to have to improvise and find a feasible work around, as well as re-level the garden, so the panels line up level on the top when fixed in place to the posts.
As a side note for the concrete posts option, if you left the posts in and fixed the wooden posts in front of them with coach bolts, and the new fence is up and looks awesome on your side, then you may encounter problems with the neighbours who are suddenly not ok with how the fence looks on their side. In this case you can either ignore them or talk nicely about building a raised wooden flowerbed on their side of the fence, flush against the fence that contrasts nicely with the concrete posts; this is always a good thing to do to keep the peace with annoying neighbours when building fences.
If you have to put new posts in, and the old posts have to come up because the new panels are longer, then you will have to be aware of tree and shrub roots, as well as rocks and even the lumps of concrete left over from the old posts if one of them lines up where one of the new posts has to go; some people even have power cables running from the house side of the garden to the shed, and you will have to watch out for them too (if in doubt check if there is any power in the shed such as a light or a power socket and follow the cable down and move it out of the way carefully).