We propose here a high-frequency spin-Hall nano-oscillator based on a simple magnetic texture, such as a domain wall, located in an antiferromagnet with an easy-axis anisotropy type. We show that the spin current, polarized along the anisotropy axis, excites a conical precession of the N\'eel vector in such a domain wall, which allows obtaining a robust ac output signal---contrary to the planar precession in a uniform uniaxial antiferromagnet, where ac output is hard to achieve. The frequency of the auto-oscillations is easily tunable by the applied current up to the terahertz range, and the threshold current vanishes for a pure uniaxial antiferromagnet. By micromagnetic simulations, we demonstrate that the pinning of the domain wall is crucial for the oscillator design, which can be achieved in the nanoconstriction layout of the free layer.