  Electronic and magnetic properties of Ga$_{1-x}$Mn$_{x}$As, obtained from
first-principles calculations employing the hybrid HSE06 functional, are
presented for $x=6.25\%$ and $12.5\%$ under pressures ranging from 0 to 15 GPa.
In agreement with photoemission experiments at ambient pressure, we find for
$x=6.25\%$ that non-hybridized Mn-3$d$ levels and Mn-induced states reside
about 5 and 0.4 eV below the Fermi energy, respectively. For elevated
pressures, the Mn-3$d$ levels, Mn-induced states, and the Fermi level shift
towards higher energies, however, the position of the Mn-induced states
relative to the Fermi energy remains constant due to hybridization of the
Mn-3$d$ levels with the valence As-4$p$ orbitals. We also evaluate, employing
Monte Carlo simulations, the Curie temperature ($T_{{\rm C}}$). At zero
pressure, we obtain $T_{{\rm C}}=181$K, whereas the pressure-induced changes in
$T_{{\rm C}}$ are d$T_{{\rm C}}$/d$p=+4.3$K/GPa for $x=12.5\%$ and an estimated
value of d$T_{{\rm C}}$/d$p\approx+2.2$K/GPa for $x=6.25\%$ under pressures up
to 6 GPa. The determined values of d$T_{{\rm C}}$/d$p$ compare favorably with
d$T_{{\rm C}}$/d$p=+$(2-3) K/GPa at $p\leq1.2$GPa found experimentally and
estimated within the $p$-$d$ Zener model for Ga$_{0.93}$Mn$_{0.07}$As in the
regime where hole localization effects are of minor importance [M.
Gryglas-Borysiewicz $et$ $al$., Phys. Rev. B ${\bf 82}$, 153204 (2010)].
