1. Remove the door from the frame, cut a caul the same width as the door out of something like 3 x 2in CLS, cut two pressure pads about the same size as the repair out of some scrap sheet material or 2 x 1 in softwood then glue the repair piece in. One pressure pad goes over the repair, the other goes at the other edge of the door on the same side in line with the first piece (hold in place with gaffer tape temporarily). The caul is then placed on top of the pads and clamped at both ends. With 3 x 2in CLS and 18mm plywood on a 35mm thick door this will require two 150mm/6in clamps
2. (Note: Requires filled repair afterwards) Cut two pieces of scrap plywood or chipboard, MDF, etc - one the size of the broken out piece, the other the same length, but 50 to 75mm wider. Drill and countersink the larger piece to take 4 to 6 screws in the overhang, about 20 to 30mm in from the edge. Glue the piece back in, apply the smaller pad and use masking tape to hold it in place. Apply the larger piece with 6 screws (this acts as a clamp) and leave to set. Once the glue has set remove, clean-up, fill holes (ideally 2-pack filler) and machine sand
3. Glue the piece back in and pin it in place by driving panel pins in through the piece (the heads of the panel pins should be left 6 to 10mm proud). Once the glue has set remove the pins using a pair of pincers. Then fill the holes, etc as above
4. Glue the piece back in and pin it in place using a second fix nail gun. Once the glue has set punch the pin heads under with a hammer and nail set. Then fill the holes, etc as above
Take your pick, but do use a waterproof glue (such as
Everbuild D4 or even Gorilla glue). The techniques above allow you to use a polyurethane (PU) glue which expands. Ideally you need a sharp hand (block) plane to flush the surface with a sander to finish it off