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 K-2 = 501 +/- 52 km s(-1) by employing the correlation between this parameter and the full width at half-maximum of the H alpha 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(M-1) = 3.2 +/- 1.0 M-circle dot. 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, M-2 <= 0.94 M-circle dot, and, in turn, on the binary mass ratio, q = M-2/M-1 <= 0.31. By exploiting the correlation between the binary inclination and the depth of the H alpha 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 M-2 = 0.5 +/- 0.3 M-circle dot, 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.