1. Assess the damage
Probe with an awl until you meet firm timber in every direction, then extend the cut-out at least 100 mm beyond that. Rot spores travel further than the discolouration suggests.
2. Cut the scarph
Use a taper of at least 8:1 — 8 times the plank thickness in length. A short, steep scarph concentrates load and will open up as the hull works.
Cut back to the centreline of a frame at each end so the new piece can be fastened to solid structure.
3. Fit the new piece
Spile the shape with a batten rather than measuring, cut slightly oversize, and plane to a dry fit with even contact across the whole scarph before any glue or bedding goes on.
4. Bond, fasten and fair
Bed with thickened epoxy or traditional compound depending on the boat's construction, clamp with even pressure, and fasten to the frames once cured.
Fair the outside with a long board so the repair follows the hull curve, then prime, fill and finish to match.
When to call a professional
If the frames behind the plank are soft, or several adjacent planks are affected, the repair becomes structural. Get a shipwright to assess before you cut.