Isoelectronic species are those that possess the same number of total electrons. Let's calculate the total number of electrons for the given species:

• $\text{NO}_3^-$: $7 \text{ (from N)} + 3 \times 8 \text{ (from O)} + 1 \text{ (from negative charge)} = 32$ electrons.
• $\text{CO}_3^{2-}$: $6 \text{ (from C)} + 3 \times 8 \text{ (from O)} + 2 \text{ (from negative charge)} = 32$ electrons.
• $\text{ClO}_3^-$: $17 \text{ (from Cl)} + 3 \times 8 \text{ (from O)} + 1 \text{ (from negative charge)} = 42$ electrons.
• $\text{SO}_3$: $16 \text{ (from S)} + 3 \times 8 \text{ (from O)} = 40$ electrons.

Thus, $\text{NO}_3^-$ and $\text{CO}_3^{2-}$ are isoelectronic.

Next, we determine their structures using VSEPR theory:

• In $\text{NO}_3^-$, the central nitrogen atom has 5 valence electrons + 1 (from charge) = 6 electrons available for bonding. It forms 3 $\sigma$ bonds with oxygen atoms (double bonds do not affect geometry) and has 0 lone pairs. Steric number = 3 ($sp^2$ hybridised), resulting in a trigonal planar geometry.
• In $\text{CO}_3^{2-}$, the central carbon atom has 4 valence electrons + 2 (from charge) = 6 electrons. It also forms 3 $\sigma$ bonds and has 0 lone pairs. Steric number = 3 ($sp^2$ hybridised), resulting in a trigonal planar geometry.

Since both have 32 electrons and a trigonal planar structure, $\text{NO}_3^-$ and $\text{CO}_3^{2-}$ are isoelectronic and isostructural.