We report cooperative magnetic orderings in a $6H$-perovskite multiferroic system, ${\mathrm{Ba}}_{3}\mathrm{Ho}{\mathrm{Ru}}_{2}{\mathrm{O}}_{9}$, via comprehensive neutron powder diffraction measurements. This system undergoes long-range antiferromagnetic ordering at ${T}_{N1}\ensuremath{\sim}50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ with a propagation wave vector of ${K}_{1}=(0.5\phantom{\rule{0.16em}{0ex}}0\phantom{\rule{0.16em}{0ex}}0)$, a transition temperature much higher than the previously reported one at \ensuremath{\sim}10 K (${T}_{N2}$). Both Ru and Ho moments order simultaneously below ${T}_{N1}$, followed by spin reorientations at lower temperatures, demonstrating strong $\mathrm{Ru}(4d)\ensuremath{-}\mathrm{Ho}(4f)$ magnetic correlation. Below ${T}_{N1}$ another magnetic phase with a propagation wave vector ${K}_{2}=(0.25\phantom{\rule{0.16em}{0ex}}0.25\phantom{\rule{0.16em}{0ex}}0)$ emerges and coexists with the one associated with ${K}_{1}$, which is rarely observed and suggests complex magnetism due to phase competition in the magnetic ground state. We argue that the exchange striction arising from the up-up-down-down spin structure associated with a ${K}_{2}$-wave vector below ${T}_{N2}$ may be responsible for the small ferroelectric polarization reported previously in this compound.