What is the standard heat of formation of the nitrate ion, based on the standard enthalpy of formation of silver nitrate?
Silver nitrate, $\ce{AgNO3}$ is a strong electrolyte. Based on the information given, I expect you are meant to assume that it dissociates completely when dissolved in water:

$$\ce{AgNO3(aq) -&gt; Ag+(aq) + NO3- (aq)}$$

Thus, we can make the assumption that $$\ce{AgNO3(aq)} \equiv \ce{Ag+(aq) + NO3- (aq)}$$

Then, we can state:

$$\Delta_\mathrm{f} H (\ce{AgNO3(aq)}) = \Delta_\mathrm{f} H (\ce{Ag+(aq)})+\Delta_\mathrm{f} H (\ce{NO3- (aq)})$$

$$\implies \pu{-99kJ/mol} = \pu{+105kJ/mol} +\Delta_\mathrm{f} H (\ce{NO3- (aq)})$$

Thus $$\Delta_\mathrm{f} H (\ce{NO3- (aq)})=\pu{-204kJ/mol}$$