Answer
Yes, $NO_{3}^{-}(aq)$ can oxidize $Mn^{2+}(aq)$ to $MnO_{4}^{-}(aq) $ under standard conditions.
Work Step by Step
$MnO_{4}^{-}(aq) + 8 H^{+}(aq) + 5e → Mn^{2+}(aq)+4 H_{2}O_{l} $ $ E^{\circ} = +1.51V$
$NO_{3}^{-}(aq) + 4 H^{+}(aq) + 3e → NO_{(g)}+ H_{2}O_{l} $ $ E^{\circ} = +0.96 V$
Since the standard reduction potential of $NO_{3}^{-}(aq) → NO_{(g)}$[+0.96 V] is less than $MnO_{4}^{-}(aq) → Mn^{2+}(aq)$ [+1.51 V], $NO_{3}^{-}(aq)$ can oxidize $Mn^{2+}(aq)$ to $MnO_{4}^{-}(aq) $ under standard conditions.
