  We show that the stability conditions on the Kuznetsov component of a
Gushel-Mukai threefold, constructed by Bayer, Lahoz, Macr\`i and Stellari, are
preserved by the Serre functor, up to the action of the universal cover of
$\text{GL}^+_2(\mathbb{R})$. As application, we construct stability conditions
on the Kuznetsov component of special Gushel-Mukai fourfolds.
