The nonlinear optical (NLO) response of the heterosystem based on nematic liquid crystal (LC) with incorporated polymer-azo-dye complex (PADC) was studied within the self-action of picosecond laser pulses at 532 nm. It was shown the enhancement of the refractive NLO response efficiency up to 20 % at lower excitation level (0.5-20 MW/cm2) and up to 5 times at higher excitation level (20-600 MW/cm2) for the PADC doped LC versus the components response and conventional azo-dye doped LC. The manifestation of three photoinduced mechanisms was observed with the rise of the PADC concentration in LC matrix: 1) orientation of the PADC; 2) trans-cis-trans isomerization; 3) cooperative response/aggregation effect. Each mechanism defines the heterosystem NLO response at corresponding PADC concentration range. The proposed smart material is promising for photonic application due to NLO properties control with variation of the PADC concentration.