A joinery shop should be able to make-up a replacement to match (ideally in hardwood) and that can be spliced into the existiing frame. Quite a skilled job, though and will require a reasonable tool kit
Depending on your DIY skills, cut back the rot, and use 2 part wood filler to repair the damage. Make sure you sand it down as it starts going off, as it ends up much harder than the original wood.
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