  The Tera-Z phase of future $e^+ e^-$ colliders, FCC-ee and CepC, is a
goldmine for exploring $Z$ portal physics. We focus on axion-like particles
(ALPs) that can be produced via $Z$ decays with a monochromatic photon. As a
template model, we consider composite Higgs models with a light pseudo-scalar
that couples through the Wess-Zumino-Witten term to the electroweak gauge
bosons. For both photophilic and photophobic cases, we show that the Tera-Z can
probe composite scales up to $100$s of TeV, well beyond the capability of the
LHC and current precision physics. Our results also apply to generic ALPs and,
in particular, severely constrain models that explain the muon $g-2$ anomaly.
