If NO3- were to get oxidised to some compound in the way SO4 2- gets oxidised to S2O8 2-, what would be that compound? In electrochemistry, we learn of the sulphate ion getting oxidised to peroxydisulphate ion. If this was to occur in the case of the nitrate ion which has a larger discharge potential, what would be formed?
First, let’s take a look at both sulfate and nitrate. They both show similar characteristics when you compare the oxidation states: remember that nitrogen is in group 15 so it has five valence electrons while sulfur is in group 16 so it has six — therefore, the highest reasonable oxidation states for these elements should be $\mathrm{+V}$ and $\mathrm{+VI}$, respectively.

$$\begin{align}&amp;\ce{\overset{$\mathrm{+V}$}{N}\overset{$\mathrm{-II}$}{O3}^-}&amp;&amp;\ce{\overset{$\mathrm{+VI}$}{S}\overset{$\mathrm{-II}$}{O4}^2-}\end{align}$$

When oxidising sulfate $\ce{SO4^2-}$ to peroxidisulfate $\ce{S2O8^2-}$, sulfur cannot be oxidised any further; the only atom that can still be oxidised is oxygen. Hence, in an initial step, we generate $\ce{SO4^{.-}}$ with three oxygens of $\mathrm{-II}$ and a fourth of $\mathrm{-I}$. Two of these then dimerise forming a peroxo-bond.

$$\ce{^-\overset{$\mathrm{-II}$}{O3}\overset{$\mathrm{+VI}$}{S}-\overset{$\mathrm{-I}$}{O}-\overset{$\mathrm{-I}$}{O}-\overset{$\mathrm{+VI}$}{S}\overset{$\mathrm{-II}$}{O3}^-}$$

Looking at nitrate, the only obvious theoretical would be to do the same, i.e. remove one oxygen electron to intermediately generate $\ce{NO3^.}$ and then have this dimerise to $\ce{O2N-O-O-NO2}$ or $\ce{N2O6}$. Interestingly, this would be a neutral compound unlike $\ce{S2O8^2-}$ which retains its charge. I don’t know whether it has been observed or not, but I would predict its formation from what I know.