  We construct the first explicit non-trivial example of deformed Hermitian
Yang-Mills (dHYM) instanton on a higher rank slope-unstable holomorphic vector
bundle over a Fano threefold. Additionally, we provide a sufficient algebraic
condition in terms of central charges for the existence of dHYM instantons on
Whitney sum of holomorphic line bundles over rational homogeneous varieties. As
a consequence, we obtain several new examples of dHYM instantons on higher rank
holomorphic vector bundles.
