We present Very Large Telescope spectroscopy, high-resolution imaging, and time-resolved photometry of KY TrA, the optical counterpart to the X-ray binary A 1524-61. We perform a refined astrometry of the field, yielding improved coordinates for KY TrA and the field star interloper of similar optical brightness that we locate 0.64 ± 0.04 arcsec SE. From the spectroscopy, we refine the radial velocity semi-amplitude of the donor star to K2 = 501 ± 52 km s-1 by employing the correlation between this parameter and the full width at half-maximum of the H α emission line. The r-band light curve shows an ellipsoidal-like modulation with a likely orbital period of 0.26 ± 0.01 d (6.24 ± 0.24 h). These numbers imply a mass function f(M1) = 3.2 ± 1.0 M⊙. The KY TrA de-reddened quiescent colour (r - i)0 = 0.27 ± 0.08 is consistent with a donor star of spectral type K2 or later, in case of significant accretion disc light contribution to the optical continuum. The colour allows us to place a very conservative upper limit on the companion star mass, M2 ≤ 0.94 M⊙, and, in turn, on the binary mass ratio, q = M2/M1 ≤ 0.31. By exploiting the correlation between the binary inclination and the depth of the H α line trough, we establish i = 57 ± 13 deg. All these values lead to a compact object and donor mass of $M_1 = 5.8^{+3.0}_{-2.4}$$\, M_\odot$ and M2 = 0.5 ± 0.3 M⊙, thus confirming the black hole nature of the accreting object. In addition, we estimate a distance towards the system of 8.0 ± 0.9 kpc.