In this paper, we consider the existence of positive solutions to mixed local and nonlocal singular quasilinear singular elliptic equations

$$\begin{array}{r}\{\begin{array}{rl}-{\mathrm{\Delta }}_{\overrightarrow{p}}u(x)+{\left(-\mathrm{\Delta }\right)}_p^{s}u(x)=\frac{f(x)}{u(x{)}^{\delta }},& x\in \mathrm{\Omega },\\ u(x)>0,& x\in \mathrm{\Omega },\\ u(x)=0,& x\in {\mathbb{R}}^N\setminus \mathrm{\Omega },\end{array}\end{array}$$

where $\mathrm{\Omega }$ is a bounded smooth domain of ${\mathbb{R}}^N(N>2)$, $-{\mathrm{\Delta }}_{\overrightarrow{p}}u$ is an anisotropic $p$-Laplace operator, $\overrightarrow{p}=(p_1,p_2,...,p_N)$ with $2\le p_1\le p_2\le \cdot \cdot \cdot \le p_N$, ${\left(-\mathrm{\Delta }\right)}_p^s$ is the fractional $p$-Laplace operator. The major results shows the interplay between the summability of the datum $f(x)$ and the power exponent $\delta$ in singular nonlinearities.