  Extensions of the Standard Model featuring excited fermions present an
interesting framework that motivates the search for exotic particles at the
LHC. Additionally, these extensions offer potential explanations for the muon's
anomalous magnetic moment and other precision observables, shedding light on
the energy scale and key parameters of the new theory. Our analysis focuses on
the one-loop radiative correction originating from excited lepton doublet and
triplet states using the effective Lagrangian approach. The bounds derived from
the $(g-2)_\mu$ anomaly can be complemented with the ones arising from other
observables like the electroweak precision observable $\Delta \rho$ and the
signals from direct LHC searches to constraint the effective theory. Our
results suggest that the $(g-2)_\mu$ anomaly can be addressed within a very
narrow region of the effective theory scale. Consequently, this imposes
indirect constraints on the parameter space of excited fermions.
