Old paddles that are well loved can start to deteriorate, but there are things you can do to fix them!
Start by removing what's left of the old finish, then clean the wood well. You'll want to use thinner for the first coat of the new varnish, brushing on the finish with the grain.
Cottage Life said, "WAIT at least 24 hours between coats, or 48 hours in damp or cool conditions. There will likely be dust nibs trapped in the underlying coats. To remove them before applying the final coat."
Whether you want to use it again on the water or use your old, loved paddle as a decoration, know that it can absolutely look beautiful again with a little work!