If you decide to buy a piece of land which benefits from planning permission you are allowed to implement that permission, in other words it does not belong in any sense to the person who applied for it.
However, you need to be very careful if you intend to make use of the drawings which formed part of the application. By buying the land you will not automatically acquire any right to use such drawings, and the starting point is that they will either belong to the person who prepared them or to the person who paid for them to be prepared, depending on the terms agreed between them. You therefore need to check, before you buy the land, to ensure that the person selling to you has the right to give you permission to use the drawings. In some cases the person who prepared them, often an architect, needs to be involved.
Sometimes the only solution is to make another, perhaps very similar application for planning permission, but one that uses new original drawings. This is of course likely to be time consuming and it will inevitably lead to additional expense.