To understand the formation of planetary systems, one needs to understand the initial conditions of planet formation, i.e. the young gas-rich planet forming disks. Spatially resolved high-contrast observations are of particular interest, since substructures in disks, linked to planet formation, can be detected and close companions or even planets in formation embedded in the disk can be revealed. In this study we present the first result of the DESTINYS survey (Disk Evolution Study Through Imaging of Nearby Young Stars). DESTINYS is an ESO/SPHERE large program that aims at studying disk evolution in scattered light, mainly focusing on a sample of low-mass stars (<1$M_odot$) in nearby (~200 pc) star-forming regions. In this particular study we present the observations of the ET Cha (RECX 15) system, a nearby old classical T Tauri star (5-8 Myr, ~100 pc), which is still strongly accreting. We use SPHERE/IRDIS in H-band polarimetric imaging mode to obtain high contrast images of the ET Cha system to search for scattered light from the circumstellar disk as well as thermal emission from close companions. We additionally employ VLT/NACO total intensity archival data taken in 2003. We report here the discovery of a low-mass (sub)stellar companion with SPHERE/IRDIS to ET Cha. We are estimating the mass of this new companion based on photometry. Depending on the system age it is a 5 Myr, 50 $M_{Jup}$ brown dwarf or an 8 Myr, 0.10 $M_odot$ M-type pre-main-sequence star. We explore possible orbital solutions and discuss the recent dynamic history of the system. Independent of the precise companion mass we find that the presence of the companion likely explains the small size of the disk around ET Cha. The small separation of the binary pair indicates that the disk around the primary component is likely clearing from the outside in, explaining the high accretion rate of the system.