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We analyse the pulsating behaviour of TIC 308396022 observed by the TESS mission. The star is a high-amplitude $\delta$ Sct star (HADS) that shows a very rich amplitude spectrum using the 3-yr light curve. Among these frequencies, the strongest peak of $f_{1}= 13.20362567(12) \rm{d^{-1}}$ is identified as the radial fundamental mode, and we also find the first and second overtones ($f_2$ and $f_3$). In the low frequency range (< 2.5 $\rm{d^{-1}}$), 22 peaks are identified to be gravity modes, which show a regular period spacing of about 2460\,s and have the angular degree $l = 1$. The period spacing pattern does not show a significant downward trend, suggesting the star rotates slowly. We note that this is a $\delta$ Sct--$\gamma$ Dor hybrid star containing a high-amplitude radial fundamental mode and a regular g-mode period spacing pattern. With O-C analysis, we find the star shows a significant time delay, implying that the star has a companion which is likely to be a white dwarf. The history of possible mass transfer provides a great opportunity to test the current theories of binary evolution, mass transfer, and pulsation., Comment: Accepted by A&A

In this paper, the pulsation behavior of high-amplitude δ Scuti star GSC 4552-1498 was analyzed. Using the high-precision photometric data from the Transiting Exoplanet Survey Satellite, two new independent frequencies F1 = 22.6424(1) day−1 and F2 = 28.6803(5) day−1 were identified for this source, along with the fundamental one F = 17.9176(7) day−1, which was previously known. In addition, the classical O − C analysis was conducted to give a new ephemeris formula of BJDmax = T 0 + P × E = 2453321.534716(4) + 0.055811(0) × E. The O − C diagram reveals a continuous period increase, but the rate of (1/P)(dP/dt) = 1.11(3) × 10−7 yr−1 seems much larger (about hundreds) than predicted by evolution theories, which is long been noticed but not well understood, possibly related to nonlinear mode interaction. Based on frequency parameters (i.e., F, F1, and F2), a series of theoretical models were conducted by employing the stellar evolution code. It turns out that F1 should be a non-radial mode and F2 is the second overtone radial mode. Due to the mass–metallicity degeneracy, the stellar parameter of the star can however not be determined conclusively. We suggest high-resolution spectral observation is highly desired in the future to further constrain models. We note GSC 4552-1498 is located on the main sequence in the H-R diagram.