  We present TOI-1259Ab, a 1.0 Rjup gas giant planet transiting a 0.74 Rsun
K-dwarf on a 3.48 day orbit. The system also contains a bound white dwarf
companion TOI-1259B with a projected distance of approximately 1600 AU from the
planet host. Transits are observed in nine TESS sector and are 2.7 per cent
deep - among the deepest known - making TOI-1259Ab a promising target for
atmospheric characterization. Our follow-up radial velocity measurements
indicate a variability of semiamplitude K = 71 m/s, implying a planet mass of
0.44 Mjup. By fitting the spectral energy distribution of the white dwarf we
derive a total age of 4.08 (+1.21 -0.53) Gyr for the system. The K-dwarf's
light curve reveals a rotational variability with a period of 28 days, which
implies a gyrochronology age broadly consistent with the white dwarf's total
age.
