Are walnuts renewable resources?

A renewable resource is a natural resource which can replenish with the passage of time, either through biological reproduction or other naturally recurring processes.

Walnuts grow on trees.
Trees replenish with the passage of time.

A walnut is an edible seed of any tree of the genus Juglans, especially the Persian or English walnut, Juglans regia. Broken nutmeats of the eastern black walnut from the tree Juglans nigra are also commercially available in small quantities, as are foods prepared with butternut nutmeats from Juglans cinerea.
Walnut seeds are a high density source of nutrients, particularly proteins and essential fatty acids. Walnuts, like other tree nuts, must be processed and stored properly. Poor storage makes walnuts susceptible to insect and fungal mold infestations; the latter produces aflatoxin—a potent carcinogen. A mold infested walnut seed batch should not be screened and then consumed; the entire batch should be discarded

so long as you set a few aside to plant new walnut trees, then yes