Pd-incorporated Zr-based metal–organic framework containing sulfone groups, named Pd(II)BUT-11, was successfully prepared by dispersing the sulfone-functionalized MOF in Pd(OAc)2 solution. X-ray diffraction, scanning electron microscopy, N2 isotherm sorption, X-ray photoelectron spectroscopy, and thermogravimetric analysis were applied to determine the features of the Pd-incorporated MOF. In the catalytic studies, Pd(II)@BUT-11 was shown to be an efficient heterogeneous catalyst for synthesizing various stilbene derivatives via the cross-coupling Heck reaction with DABCO-derived deep eutectic solvent (DES) as a green solvent. Notably, the catalyst and the solvent could be recovered and reused, with their activity and structure remaining stable throughout several trials. The method provides an alternative solution to the conventional catalysts and solvents, resulting in a green and efficient stilbene synthesis process. Furthermore, the stilbenes were separated by extraction with ethyl acetate due to the low solubility of DES with this solvent.