Inelastic neutron scattering has been employed to study in detail the low-energy crystal-field (CEF) excitations of Ho³⁺ in tetragonal antiferromagnetic (AF) Ho_0.1Y_0.9Ba₂Cu₃O_6.13. We observe a splitting of the lowest excited Γ₅ doublet at T=1.5 K. This splitting is explained as resulting from the exchange interaction with the AF subsystem of copper spins. The corresponding susceptibility at the Ho³⁺ site has a symmetry lower than the tetragonal one of the CEF potential and, as a result, produces the splitting. The value of the coupling between Ho³⁺ and Cu²⁺ ions J_ex=2.4 meV is derived from the experimentally observed value of the splitting ΔE=0.1 meV and parameters of the AF subsystem, known from the neutron scattering experiments. Some possible consequences of the rare-earth (RE)-copper exchange are discussed, including the interaction between RE ions via the virtual exchange by spin waves.