I am running 

5.8.0-kali2-amd64

I have tried using this driver T4U_V3_181018_Linux_beta.zip and followed the instructions in Linux Installation Guide under Kali 2018.1 (was developed for Kernel source version 4.14.0-kali3-amd64)

I am getting the following error:

kali@kali:~/source-code/T4Uv3_WiFi_linux_v5.3.1_beta$ dpkg-query -s linux-headers-$(uname -r)

Package: linux-headers-5.8.0-kali2-amd64
Status: install ok installed
Priority: optional
Section: kernel
Installed-Size: 5701
Maintainer: Kali Developers devel@kali.org
Architecture: amd64
Source: linux
Version: 5.8.10-1kali1
Depends: linux-headers-5.8.0-kali2-common (= 5.8.10-1kali1), linux-kbuild-5.8 (>= 5.8.10-1kali1), linux-compiler-gcc-10-x86
Description: Header files for Linux 5.8.0-kali2-amd64
This package provides the architecture-specific kernel header files for
Linux kernel 5.8.0-kali2-amd64, generally used for building out-of-tree
kernel modules. These files are going to be installed into
/usr/src/linux-headers-5.8.0-kali2-amd64, and can be used for building
modules that load into the kernel provided by the
linux-image-5.8.0-kali2-amd64 package.
Homepage: kali.org

kali@kali:~/source-code/T4Uv3_WiFi_linux_v5.3.1_beta$ make

make ARCH=x86_64 CROSS_COMPILE= -C /lib/modules/5.8.0-kali2-amd64/build M=/home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta modules
make[1]: Entering directory '/usr/src/linux-headers-5.8.0-kali2-amd64'
CC [M] /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/core/rtw_cmd.o
In file included from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/drv_types.h:30,
from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/core/rtw_cmd.c:17:
/home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/wifi.h:1031: warning: "IEEE80211_MAX_AMPDU_BUF" redefined
1031 | #define IEEE80211_MAX_AMPDU_BUF 0x40
|
In file included from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/osdep_service_linux.h:83,
from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/osdep_service.h:50,
from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/drv_types.h:27,
from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/core/rtw_cmd.c:17:
/usr/src/linux-headers-5.8.0-kali2-common/include/linux/ieee80211.h:1600: note: this is the location of the previous definition
1600 | #define IEEE80211_MAX_AMPDU_BUF 0x100
|
In file included from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/drv_types.h:78,
from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/core/rtw_cmd.c:17:
/home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/rtw_security.h:252:8: error: redefinition of ‘struct sha256_state’
252 | struct sha256_state {
| ^~~~~~~~~~~~
In file included from /usr/src/linux-headers-5.8.0-kali2-common/include/linux/filter.h:23,
from /usr/src/linux-headers-5.8.0-kali2-common/include/net/sock.h:59,
from /usr/src/linux-headers-5.8.0-kali2-common/include/linux/tcp.h:19,
from /usr/src/linux-headers-5.8.0-kali2-common/include/linux/ipv6.h:88,
from /usr/src/linux-headers-5.8.0-kali2-common/include/net/addrconf.h:50,
from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/osdep_service_linux.h:48,
from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/osdep_service.h:50,
from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/include/drv_types.h:27,
from /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/core/rtw_cmd.c:17:
/usr/src/linux-headers-5.8.0-kali2-common/include/crypto/sha.h:84:8: note: originally defined here
84 | struct sha256_state {
| ^~~~~~~~~~~~
make[3]: *** [/usr/src/linux-headers-5.8.0-kali2-common/scripts/Makefile.build:286: /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta/core/rtw_cmd.o] Error 1
make[2]: *** [/usr/src/linux-headers-5.8.0-kali2-common/Makefile:1764: /home/kali/source-code/T4Uv3_WiFi_linux_v5.3.1_beta] Error 2
make[1]: *** [/usr/src/linux-headers-5.8.0-kali2-common/Makefile:185: __sub-make] Error 2
make[1]: Leaving directory '/usr/src/linux-headers-5.8.0-kali2-amd64'
make: *** [Makefile:1999: modules] Error 2