Superexchange interaction in insulating <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>EuZn</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

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.