VLT/UVES spectroscopic and TESS photometric observations for WASP 0346-21 allow the direct determination of its physical properties, along with the detection of a circumbinary object and oscillating signals. The high-resolution spectra yielded the radial velocities of all three stars and the atmospheric parameters of Teff,A = 7225±42 K, [M/H] = 0.30±0.03 dex, and vAsin i$ = 78$±$5 km s$⁻¹$ of the primary component. The combined analysis of these observations resulted in the fundamental parameters of the eclipsing components and the third light of $l_3$ = 0.043$±$0.004, which is consistent with the light contribution of the tertiary star observed in the echelle spectra. WASP 0346-21 A resides within the overlapping main-sequence domain of $δ$ Sct and $γ$ Dor variables, while the secondary component of $MB$ = 0.185$±$0.013 M$_$, $RB$ = 0.308$±$0.023 R$_$, $Teff,B$ = 10,655$±$146 K, and $LB$ = 1.09$±$0.17 L$_$ matches well with the low-mass white dwarf (WD) model for $Z$ = 0.01, corresponding to the thick-disk population classified by the Galactic kinematics. Multifrequency analyses were performed on the residual TESS data after removing the binarity effects. The low frequencies around 26.348 day⁻¹ and 17.683 day⁻¹ are δ Sct pulsations originating from WASP 0346-21 A, and the high frequencies of 97.996 day⁻¹ and 90.460 day⁻¹ are considered to be extremely low-mass WD oscillations. These results demonstrate that WASP 0346-21 is a hierarchical triple system, consisting of an EL CVn binary with multiperiodic pulsations in each component and a distant outer tertiary.
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