The piezoelectric effect in novel 1–3-type composites with lead-free components is studied in terms of the effective piezoelectric coefficients d3j* and g3j*, electromechanical coupling factors k3j* and anisotropy factors d33* / d31* and k33* / k31*. The piezoelectric component is either a domain-engineered -poled single crystal or a poled ceramic, and both the single crystal and ceramic are based on ferroelectric alkali-niobate—alkali-tantalate solid solutions. In the studied composites this component represents a system of long rods that are oriented parallel to the poling axis OX3, and the rods are surrounded by a large piezo-passive polymer matrix that can be either monolithic (in 1–3 composites) or porous (in 1–3–0 composites). The high level of piezoelectric sensitivity of the lead-free 1–3 and 1–3–0 composites is noted due to the longitudinal piezoelectric coefficient g33* ~ 102–103 mV.m / N. Conditions for a large anisotropy d33∗ / | d31∗ | = g33* / | g31* | ≥ 5 and k33* / | k31* | ≥ 5 are valid in specific volume-fraction ranges of the ferroelectric component and porosity in the polymer component. The important role of the pore shape in achieving the large anisotropy of d3j* and k3j* of the 1–3–0 composite is discussed. The studied 1–3-type composites are of interest for the selection of advanced piezoelectric materials for transducer, sensor and related applications, with additional respect to the environment due to the lead-free nature of the composite components.