  Alternative magnetic materials or ``altermagnets", characterized by their
non-relativistic, momentum-dependent spin-split states, represent a
cutting-edge advancement in the field of magnetism, offering promising avenues
for spintronic applications. Among these materials, hexagonal MnTe has emerged
as a standout material candidate for its substantial spin-splitting. In this
study, employing first-principles electronic structure calculations and spin
group symmetry analysis, we delve into the interplay of altermagnetism and
pressure in two main phases of MnTe. Our relativistic calculations demonstrate
the presence of tunable anomalous Hall effect (AHE) in hexagonal MnTe. In
addition, our results underscore the pivotal role of pressure as a tuning
parameter for the alternative magnetic traits in the system. Furthermore, we
identify another phase of MnTe with orthorhombic structure, namely
$\gamma$-MnTe, hosting altermagnetic characteristics. We study, in detail, its
response in AHE and spin-spliting due to magnetization and pressure variations,
respectively. Our study highlights the substantial impact of pressure on the
properties of alternative magnetic materials, particularly emphasizing the
pronounced tuning effect observed in the hexagonal and orthorhombic MnTe.
