Recent numerical results [Gonzalez et al., Phys. Rev. Lett. 122, 017201 (2019), 10.1103/PhysRevLett.122.017201; Shimada et al., J. Phys. Conf. Ser. 969, 012126 (2018), 10.1088/1742-6596/969/1/012126] point to the existence of a partial-disorder ground state for a spin-1/2 antiferromagnet on the stuffed honeycomb lattice, with 2/3 of the local moments ordering in an antiferromagnetic Néel pattern, while the remaining 1/3 of the sites display short-range correlations only, akin to a quantum spin liquid. We derive an effective model for this disordered subsystem, by integrating out fluctuations of the ordered local moments, which yield couplings in a formal 1 /S expansion, with S being the spin amplitude. The result is an effective triangular-lattice XXZ model, with planar ferromagnetic order for large S and a stripe-ordered Ising ground state for small S , the latter being the result of frustrated Ising interactions. Within the semiclassical analysis, the transition point between the two orders is located at Sc=0.646 , being very close to the relevant case S =1 /2 . Near S =Sc quantum fluctuations tend to destabilize magnetic order. We conjecture that this applies to S =1 /2 , thus explaining the observed partial-disorder state.