$\text{AgN}{\text{O}}_3+\text{KCl}\left(\text{aq}\right)\to \text{AgCl}\left(\mathrm{s}\right)+\text{KN}{\text{O}}_3\left(\text{aq}\right)$

Initially there is aq. $\mathrm{K}\mathrm{C}\mathrm{l}$ solution now as solution of $\text{AgN}{\text{O}}_3$ is added, $\mathrm{A}\mathrm{g}\mathrm{C}\mathrm{l}\left(\mathrm{s}\right)$ is formed. Hence conductivity of solution is almost compensated (or slightly increase) by the formation of $\text{KN}{\text{O}}_3$ . After end point conductivity increases more rapidly because addition of excess $\text{AgN}{\text{O}}_3$ solution.