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The $^{24}$Mg($p$, $\alpha$)$^{21}$Na reaction was measured at the HolifieldRadioactive Ion Beam Facility at Oak Ridge National Laboratory in order tobetter constrain spins and parities of energy levels in $^{21}$Na for theastrophysically important $^{17}$F($\alpha, p$)$^{20}$Ne reaction ratecalculation. 31 MeV proton beams from the 25-MV tandem accelerator and enriched$^{24}$Mg solid targets were used. Recoiling $^{4}$He particles from the$^{24}$Mg($p$, $\alpha$)$^{21}$Na reaction were detected by a highly segmentedsilicon detector array which measured the yields of $^{4}$He particles over arange of angles simultaneously. A new level at 6661 $\pm$ 5 keV was observed inthe present work. The extracted angular distributions for the first four levelsof $^{21}$Na and Distorted Wave Born Approximation (DWBA) calculations werecompared to verify and extract angular momentum transfer.

$^{24}$Mg($p$, $\alpha$)$^{21}$Na reaction study for spectroscopy of $^{21}$Na