How to Design a Pre-emphasis filter knowing the gain, a zero and a pole?
Traditionally, these filters were implemented as analog filters, and they are different from the usual discrete-time first-order FIR pre-emphasis filter used in speech processing.

The transfer function of such an analog pre-emphasis filter is

$$H(s)=g\frac{1+s\tau_1}{1+s\tau_2},\qquad\tau_1\gt\tau_2,\tag{1}$$

where $g$ is the DC gain, and $\tau_1$ and $\tau_2$ are two time constants determining the locations of the zero and the pole:

$$s_0=-\frac{1}{\tau_1}\\s_{\infty}=-\frac{1}{\tau_2}\tag{2}$$

If the pole (or the zero) are given in terms of frequencies $f_i$, then the following relation holds:

$$\tau_i=\frac{1}{2\pi f_i},\qquad i\in\{1,2\}\tag{3}$$

So for a given frequency $f_i$ you can use $(3)$ to determine the corresponding time constant, from which you obtain the desired transfer function $(1)$.

If you want to implement that filter in discrete time, the most common option is to use the bilinear transform:

$$s=\frac{2}{T}\frac{z-1}{z+1}\tag{4}$$

where $T$ is the sampling period, i.e., the inverse of the sampling frequency. Note that $(2)$ is the bilinear transform without pre-warping, which means that the frequency axis will be warped, so neither the pole frequency nor the zero frequency of the analog filter will be exactly realized in the discrete-time domain. You can pre-warp the analog frequencies (or time constants) to make sure that the resulting discrete-time filter has the desired pole and zero frequencies. In order to realize a (pole or zero) frequency $f_i$ in the discrete-time domain, you need to use the following time constant in the analog filter transfer function $(1)$:

$$\tau_i=\frac{T}{2\tan\left(\frac{\pi f_i}{f_s}\right)}\tag{5}$$

where $f_s=1/T$ is the sampling frequency.

You can find more information on pre-warping in this answer.