We consider the possibility of texture zeros in lepton mass matrices of the minimal left-right symmetric model (LRSM) where light neutrino mass arises from a combination of type I and type II seesaw mechanisms. Based on the allowed texture zeros in light neutrino mass matrix from neutrino and cosmology data, we make a list of all possible allowed and disallowed texture zeros in Dirac and heavy neutrino mass matrices which appear in type I and type II seesaw terms of LRSM. For the numerical analysis we consider those cases with maximum possible texture zeros in light neutrino mass matrix $M_{ u}$, Dirac neutrino mass matrix $M_D$, heavy neutrino mass matrix $M_{RR}$ while keeping the determinant of $M_{RR}$ non-vanishing, in order to use the standard type I seesaw formula. The possibility of maximum zeros reduces the free parameters of the model making it more predictive. We then compute the new physics contributions to rare decay processes like neutrinoless double beta decay, charged lepton flavour violation. We find that even for a conservative lower limit on a left-right symmetry scale corresponding to heavy charged gauge boson mass 4.5 TeV, in agreement with collider bounds, for right-handed neutrino masses above 1 GeV, the new physics contributions to these rare decay processes can saturate the corresponding experimental bound.
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