  We report magnetic and transport properties of single-crystalline
EuZn$_{2}$P$_{2}$, which has trigonal CaAl$_2$Si$_2$-type crystal structure and
orders antiferromagnetically at $\approx$23~K. Easy $ab$-plane
magneto-crystalline anisotropy was confirmed from the magnetization isotherms,
measured with a magnetic field applied along different crystallographic
directions ($ab$-plane and $c$-axis). Positive Curie-Weiss temperature
indicates dominating ferromagnetic correlations. Electrical resistivity
displays insulating behavior with a band-gap of $\approx\,$0.177~eV, which
decreases to $\approx\,$0.13~eV upon application of a high magnetic field. We
explained the intriguing presence of magnetic interactions in an intermetallic
insulator by the mechanism of extended superexchange, with phosphorus as an
anion mediator, which is further supported by our analysis of the charge and
spin density distributions. We constructed the effective Heisenberg model, with
exchange parameters derived from the \textit{ab initio} DFT calculations, and
employed it in Monte-Carlo simulations, which correctly reproduced the
experimental value of N\'eel temperature.
