a panel is difficult to carry. Although reasonably light, it will try to fly away from a roof rack, and won't fit in a car.
If you have wooden posts either side, and can use a saw, you may be able to buy a couple of decking boards. These are very light and easy to carry. Budget versions will do. You can screw these to your existing fence posts, one at the top and one about a foot up from the bottom, and fill between them with whatever you can get. Even pallets would do (but you will need a central board as well for short pieces). If you find a DIY shed willing to cut boards to a size that will fit in your car, you could use OSB pieces and screw through them into the horizontal boards. Sheet materials usually come in pieces 2440x1220mm (smaller pieces are more expensive) so you would need two. Ply is unsuitable because if rain and damp penetrate the edges, it will peel apart. The bigger the pieces are, the more rigid it will be. It will be stronger than your old fence panels.
If you still have the remains of your old panel, you could screw through its battens it to the horizontal boards I describe.
If you can get decking boards delivered at an attractive price, you can use them as planks between your posts, and screw them horizontally to board the whole gap. This makes a very strong fence, and the size and weight of each individual board makes it very easy to build. You will need about 14 boards. A budget range or seconds will do since you will not be standing on them. Avoid long boards as you will have to cut them and there will be waste.
This is a cheap one www.wickes.co.uk/Wickes-Deck-Board---25mm-x-120mm-x-1-8m/p/145255 but check it is long enough to span over bothfence posts or you will need brackets and the longer one will be better www.wickes.co.uk/Wickes-Deck-Board---25mm-x-120mm-x-2-4m/p/114551
There may be a decking merchant or woodyard local to you that is open.
You will need some fence stain to make the job look decent. Preferably a dark colour which will hide rough work.
If this appeals, come back and I will tell you more about the screws and drill you will need. You will need a spirit level for the bottom board.