A second extragalactic pulsar wind nebula (PWN) is discovered in the MeV-GeV band using the Fermi-LAT. Faint, point-like $\gamma$-ray emission is detected at the location of the composite supernova remnant (SNR) B0453-685 from energies 300 MeV - 2 TeV. The Fermi-LAT data analysis of the new $\gamma$-ray source is presented together with a detailed multi-wavelength investigation to understand the nature of the observed emission. The observational evidence and physical implications from broadband modeling do not support an SNR $\gamma$-ray origin. Semi-analytic radiative evolutionary models are explored to understand the potential for any pulsar or PWN component responsible for the observed $\gamma$-ray emission. The modeling results favor an evolved PWN ($\tau\sim 14,000$ years) that has been impacted by the return of the SNR reverse shock with a possible substantial pulsar component below $5$ GeV. The particle acceleration mechanisms and their efficiency within B0453-685 have important implications for the role PWNe play in generating Cosmic Rays (CRs), but constraints on the synchrotron cut-off are required to accurately characterize the underlying particle properties.