The low-temperature magnetic properties of tcr{polycrystalline} Na$_2$IrO$_3$, a candidate material for the realization of a quantum spin-liquid state, were investigated by means of muon-spin relaxation and nuclear magnetic resonance methods under chemical and hydrostatic pressure. The Li-for-Na chemical substitution promotes an inhomogeneous magnetic order, whereas hydrostatic pressure (up to 3.9,GPa) results in an enhancement of the ordering temperature $T_mathrm{N}$. In the first case, the inhomogeneous magnetic order suggests either short- or long-range correlations of broadly distributed $j=,$textonehalf Ir$^{4+}$ magnetic moments, reflecting local disorder. The increase of $T_mathrm{N}$ under applied pressure points at an increased strength of three dimensional interactions arising from interlayer compression.
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