The reaction, ${\mathrm{NH}}_4^{+}+{\mathrm{CN}}^{-}\rightleftharpoons \mathrm{HCN}\left(\mathrm{aq}\right)+{\mathrm{NH}}_3\left(\mathrm{aq}\right)$ proceeds in

${\mathrm{NH}}_4^{+}+{\mathrm{CN}}^{-}\rightleftharpoons \mathrm{HCN}\left(\mathrm{aq}\right)+{\mathrm{NH}}_3\left(\mathrm{aq}\right)$

As ${\mathrm{NH}}_3$ is a weak base and HCN is a weak acid. Backward reaction do not takes place because both are weak and HCN do not give ${\mathrm{H}}^{+} \mathrm{ion} \mathrm{to} {\mathrm{NH}}_3$ to make a backward reaction. Hence forward reaction occurs.