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Let $\pi$ be a unitary cuspidal automorphic representation of$\text{GL}_{4}(\mathbb{A}_{\mathbb{Q}})$. Let $f \geq 1$ be given. We show thatthere exists infinitely many primitive even (resp. odd) Dirichlet characters$\chi$ with conductor co-prime to $f$ such that $L(s, \pi \otimes \chi)$ isnon-vanishing at the central point.  Our result has applications for the construction of $p$-adic $L$-functionsfor $\text{GSp}_{4}$ following Loeffler-Pilloni-Skinner-Zerbes, the Bloch-Katoconjecture and the Birch-Swinnerton-Dyer conjecture for abelian surfacesfollowing Loeffler-Zerbes, strong multiplicity one results for paramodularcuspidal representations of $\text{GSp}_{4}(\mathbb{A}_{\mathbb{Q}})$ and therationality of the central values of $\text{GSp}_{4}(\mathbb{A}_{\mathbb{Q}})$$L$-functions in the remaining non-regular weight case.

Non-vanishing of twists of $\text{GL}_4(\mathbb{A}_{\mathbb{Q}})$ $L$-functions