Despite an apparent ban being introduced in 2002, fox hunts continue by exploiting loopholes in the legislation.
Green MSP Alison Johnstone proposed a bill in 2019 to close the loopholes and also protect mountain hares.
The hare protection was won and now the party has pledged to finish the job.
Laura Moodie, who is also first on the South Scotland list, said: "Most people think fox-hunting is already banned in Scotland, but loopholes in the law mean hunting continues much as it did .
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"We will close all of the loopholes and end all hunting with dogs for good."