If you’re fishing in the Canaries and have a licence issued by another Spanish autonomous government, such as the Cantabria fishing licence, you can fish without any problem.
On their Fishing Dept. Canary Islands government website, in the frequently asked questions, you can read the following:
This translates to:
Fishing in the Canaries: Difference Between “Interior Waters” and “Exterior Waters”
When fishing in the Canaries, you must know the difference between “interior” and “exterior” waters.
“Interior waters” are the ones nearer to the shoreline. In Spanish, they’re called “aguas interiores”. If you draw a straight line that joins all the parts of an island that “stick out”, you will have the boundary between interior and exterior waters. The Canary Islands government is in charge of taking care of what goes on here.
“Exterior waters” or “Aguas exteriores” are the ones located further away from the shoreline, after you’ve drawn the line from the points that “stick out” in the map. The Spanish government takes care of these.
Fishing limits i.e. maximum kilos of fish per person/day can vary a little between the two areas, but are usually almost the same.
