  Ga for Mn substitution in multiferroic TbMnO$_{3}$ has been performed in
order to study the influence of Mn-magnetic ordering on the Tb-magnetic
sublattice. Complete characterization of TbMn$_{1-x}$Ga$_x$O$_{3}$ ($x$ = 0,
0.04, 0.1) samples, including magnetization, impedance spectroscopy, and x-ray
resonant scattering and neutron diffraction on powder and single crystals has
been carried out. We found that keeping the same crystal structure for all
compositions, Ga for Mn substitution leads to the linear decrease of $T_{\rm
N}^{\rm Mn}$ and $\tau^{\rm Mn}$, reflecting the reduction of the exchange
interactions strength $J_{\rm Mn-Mn}$ and the change of the Mn-O-Mn bond
angles. At the same time, a strong suppression of both the induced and the
separate Tb-magnetic ordering has been observed. This behavior unambiguously
prove that the exchange fields $J_{\rm Mn-Tb}$ have a strong influence on the
Tb-magnetic ordering in the full temperature range below $T_{\rm N}^{\rm Mn}$
and actually stabilize the Tb-magnetic ground state.
