Digital filter coefficients from low-pass to high-pass
You can apply a so-called all-pass transformation to a discrete-time low-pass prototype filter in order to convert it to other standard filters (such as high-pass, band-pass, and band-stop). This is accomplished by transforming the complex variable $z$ in the transfer function of the prototype filter by a function $G(z)$ which satisfies $|G(e^{j\omega})|=1$, i.e., $G(z)$ is an all-pass function. This makes sure that the transformation maps the unit circle onto itself, i.e., the frequency response of the new filter is just a shifted and/or warped version of the prototype frequency response.
The most straightforward way to transform a discrete-time low-pass filter to a high-pass filter is to use the trivial transform $G(z)=-z$, i.e.,
$$H_{HP}(z)=H_{LP}(-z)\tag{1}$$
If $H_{LP}(z)$ is given by
$$H_{LP}(z)=\frac{\displaystyle\sum_{k=0}^Nb[k]z^{-k}}{\displaystyle 1+\sum_{k=1}^{N}a[k]z^{-k}}\tag{2}$$
then $H_{HP}(z)$ becomes
$$H_{HP}(z)=\frac{\displaystyle\sum_{k=0}^N(-1)^kb[k]z^{-k}}{\displaystyle 1+\sum_{k=1}^{N}(-1)^ka[k]z^{-k}}\tag{3}$$
This transformation shifts the low-pass frequency response by $\pi$ (i.e., by half the sampling frequency). Consequently, if $\omega_c$ is the cut-off frequency of the low-pass prototype filter, the cut-off frequency of the resulting high-pass filter is given by $\omega'_c=\pi-\omega_c$.
Other cut-off frequencies can be obtained by applying the more general lowpass-to-highpass transformation
$$G(z)=-\frac{z+\alpha}{1+\alpha z},\qquad |\alpha|&lt;1\tag{4}$$
The simple transformation shown above is obtained from $(4)$ by the choice $\alpha=0$.
This and other frequency transformations applicable to discrete-time filters are treated in some detail in Chapter $7.4$ of the third edition of Oppenheim and Schafer's Discrete-Time Signal Processing.
Also take a look at these related questions and their answers: Q1, Q2.