  Realization of the quantum anomalous Hall effect and axion electrodynamics in
topological materials are among the paradigmatic phenomena in condensed matter
physics. Recently, signatures of both phases are observed to exist in thin
films of MnBi$_2$Te$_4$, a stoichiometric antiferromagnetic topological
insulator. Direct evidence of the bulk topological magnetoelectric response in
an axion insulator requires an energy gap at its topological surface state
(TSS). However, independent spectroscopic experiments revealed that such a
surface gap is absent, or much smaller than previously thought, in
MnBi$_2$Te$_4$. Here, we utilize angle resolved photoemission spectroscopy and
density functional theory calculations to demonstrate that a sizable TSS gap
unexpectedly exists in Sb-doped MnBi$_2$Te$_4$. This gap is found to be
topologically nontrivial, insensitive to the bulk
antiferromagnetic-paramagnetic transition, while enlarges along with increasing
Sb concentration. Our work shows that Mn(Bi$_{1-x}$Sb$_x$)$_2$Te$_4$ is a
potential platform to observe the key features of the high-temperature axion
insulator state, such as the topological magnetoelectric responses and
half-integer quantum Hall effects.
