We present a photometric analysis of the Transiting Exoplanet Survey Satellite (TESS) light curve of contact binary system DY Cet and the behavior of its orbital period variation. The light curve and published radial velocity data analysis was performed using the Wilson-Devinney code. As a result of simultaneous analysis of the light curve with radial velocity data, the masses and radii of the system's components were determined as M (1) = 1.55 +/- 0.02 M (circle dot), M (2) = 0.55 +/- 0.01 M (circle dot) and R (1) = 1.51 +/- 0.02 R (circle dot), R (2) = 0.95 +/- 0.02 R (circle dot), respectively. The degree of contact (f) and mass ratio (q) of the system were determined as 23% and 0.355 +/- 0.012, respectively. Orbital period analysis of DY Cet was conducted for the first time in this study. It was observed that the orbital period has a sinusoidal change with decreasing parabola. To explain the orbital period change, mass transfer between components is proposed with the assumption of conservative mass, and the transfer rate was calculated to be dM/dt = 1.1 x 10(-7) M (circle dot) yr(-1). A possible third component is suggested for explaining the sinusoidal change, and the mass of the unseen component was determined as 0.13 M (circle dot). The age of the DY Cet system was estimated as 3.77 Gyr.