  We construct new black brane solutions in the context of Horndeski gravity,
in particular in its K-essence sector. These models are supported by axion
scalar fields that depend only on the horizon coordinates. The dynamics of
these fields is determined by a K-essence term that includes the standard
kinetic term $X$ and a correction of the form $X^{k}$. We find both neutral and
charged exact and analytic solutions in $D$-dimensions, which are
asymptotically anti de Sitter. Then, we describe in detail the thermodynamical
properties of the four-dimensional solutions and we compute the dual
holographic DC conductivity.
