Recently, intercalation emerges as an effective way to manipulate ground-state properties and enrich quantum phase diagrams of layered transition metal dichalcogenides (TMDCs). In this work, we focus on fully Ta-intercalated bilayer $2H\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ with a stoichiometry of ${\mathrm{Ta}}_{3}{\mathrm{S}}_{4}$, which has recently been experimentally synthesized. Based on first-principles calculations, we computationally show the suppression of an intrinsic $3\ifmmode\times\else\texttimes\fi{}3$ charge-density wave (CDW) in the ${\mathrm{TaS}}_{2}$ layer, and the emergence of a $2\ifmmode\times\else\texttimes\fi{}1$ CDW in intercalated Ta layer. The formation of the CDW in ${\mathrm{Ta}}_{3}{\mathrm{S}}_{4}$ is triggered by strong electron-phonon coupling (EPC) between the $d$-like orbitals of intercalated Ta atoms via the imaginary phonon modes at $M$ point. A $2\ifmmode\times\else\texttimes\fi{}1$ CDW structure is identified, featuring quasi-one-dimensional Ta chains, attributable to the competition between the CDW displacements associated with potential CDW vectors (${\mathbit{q}}_{\text{CDW}}\mathrm{s}$). Superconductivity is found to coexist with the $2\ifmmode\times\else\texttimes\fi{}1$ CDW in ${\mathrm{Ta}}_{3}{\mathrm{S}}_{4}$, with an estimated superconducting transition temperature (${T}_{\mathrm{c}}$) of 3.0 K, slightly higher than that of bilayer ${\mathrm{TaS}}_{2}$. The ${\mathrm{Ta}}_{3}{\mathrm{S}}_{4}$ structures of non-CDW, $2\ifmmode\times\else\texttimes\fi{}1$ CDW, and $2\ifmmode\times\else\texttimes\fi{}2$ CDW can be switched by strain. Our work enriches the phase diagram of ${\mathrm{TaS}}_{2}$, offers a candidate material for studying the interplay between CDW and superconductivity, and highlights intercalation as an effective way to tune the physical properties of layered materials.

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