$ sudo apt update
$ sudo apt install software-properties-common
$ sudo add-apt-repository ppa:ubuntugis/ppa
$ sudo apt update
$ sudo apt install libgdal-dev gdal-bin
After that, you should be able to get the installed GDAL version:
$ ogrinfo --version
Then, you need to set some environment variables:
$ export CPLUS_INCLUDE_PATH=/usr/include/gdal
$ export C_INCLUDE_PATH=/usr/include/gdal
$ [sudo] pip install GDAL==$(ogrinfo --version | cut -d' ' -f2 | cut -d',' -f1)