Precision measurements of the $\vert V_{cs} \vert$ matrix element are crucial to test the unitarity of the CKM matrix. $D$ and $D_s$ decays are one of the best environments to perform such measurements. Moreover, an improved knowledge of the $D$/$D_s$ decay can help to calibrate the LQCD calculations. The BESIII Experiment at Beijing Electron Positron Collider II (BEPC-II) has accumulated the world$'$s largest $e^+e^-$ collision samples at 3.773 and 4.178 GeV. In this presentation, we report the measurement of leptonic and semileptonic $D^{0(+)}$ and $D_s$ decay at BESIII, with focus on $\vert V_{cs} \vert$ determination, form factor and decay constant estimations. In addition, we report the LFU test in $D \rightarrow \pi l \nu$ decays.