A search for the exotic decay of the Higgs boson (H) into a b$ \overline{b} $ resonance plus missing transverse momentum is described. The search is performed with the ATLAS detector at the Large Hadron Collider using 139 fb$^{−1}$ of pp collisions at $ \sqrt{s} $ = 13 TeV. The search targets events from ZH production in an NMSSM scenario where H → $ {\overset{\sim }{\chi}}_2^0{\overset{\sim }{\chi}}_1^0 $, with $ {\overset{\sim }{\chi}}_2^0 $→$ a{\overset{\sim }{\chi}}_1^0 $, where a is a light pseudoscalar Higgs boson and $ {\overset{\sim }{\chi}}_{1,2}^0 $ are the two lightest neutralinos. The decay of the a boson into a pair of b-quarks results in a peak in the dijet invariant mass distribution. The final-state signature consists of two leptons, two or more jets, at least one of which is identified as originating from a b-quark, and missing transverse momentum. Observations are consistent with Standard Model expectations and upper limits are set on the product of cross section times branching ratio for a three-dimensional scan of the masses of the $ {\overset{\sim }{\chi}}_2^0 $, $ {\overset{\sim }{\chi}}_1^0 $ and a boson.