Writing the O.N. of all the atoms above their symbols, we have
O.N. of Zn changes from zero in Zn to +2 in Zn2+ and, therefore, it is oxidized and hence Zn acts as a reductant.
The O.N. of N decreases from +5 in NO3– to -3 in NO4+ and, therefore, it is reduced and hence NO3– acts as the oxidant.