In an electrolytic cell of $\mathrm{Ag}/{\mathrm{AgNO}}_3/\mathrm{Ag}$, when current is passed, the concentration of ${\mathrm{AgNO}}_3$

At anode $\mathrm{Ag}\to {\mathrm{Ag}}^{+}+{\mathrm{e}}^{-}$

At cathode ${\mathrm{Ag}}^{+}+{\mathrm{e}}^{-}\to \mathrm{Ag}$

Number of equivalents of Ag oxidised = Number of equivalnts of Ag⁺ reduced

So concentration of ${\mathrm{Ag}}^{+}$ will remain same.