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We analyse the pulsating behaviour of TIC 308396022 observed by the TESSmission. The star is a high-amplitude $\delta$ Sct star (HADS) that shows avery rich amplitude spectrum using the 3-yr light curve. Among thesefrequencies, the strongest peak of $f_{1}= 13.20362567(12) \rm{d^{-1}}$ isidentified as the radial fundamental mode, and we also find the first andsecond 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 aregular 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 fundamentalmode and a regular g-mode period spacing pattern. With O-C analysis, we findthe star shows a significant time delay, implying that the star has a companionwhich is likely to be a white dwarf. The history of possible mass transferprovides a great opportunity to test the current theories of binary evolution,mass transfer, and pulsation.

TIC 308396022: a $\delta$ Scuti--$\gamma$ Doradus hybrid with large-amplitude radial fundamental mode and regular g-mode period spacing