We quantify the anomalous magnetic moment and electric dipole moment of the $\tau$-lepton through the process
$e^{+}e^{-} \rightarrow \tau^+ \tau^-\gamma$, within the ranges of energies and luminosities affordable at the
future International Linear Collider (ILC) and the Compact Linear Collider (CLIC).
The tau-lepton is a key particle in various Beyond the Standard Model
(BSM) models and is considered a laboratory for many experimental or simulation aspects
in searches for new physics. In particular, the tau-lepton anomalous couplings to bosons
in the $\tau^+ \tau^- \gamma$ and $\tau^+ \tau^- Z$ vertices, have made the tau-lepton
one of the most attractive particles for new physics searches.