You can get it by installing libqtwebkit4:
sudo apt install libqtwebkit4
To figure out which package provides a particular file, you can use apt-file (install it by running sudo apt install apt-file). For the case of libQtWebKit.so.4:
$ apt-file search libQtWebKit.so.4
libqtwebkit4: /usr/lib/x86_64-linux-gnu/libQtWebKit.so.4
libqtwebkit4: /usr/lib/x86_64-linux-gnu/libQtWebKit.so.4.10
libqtwebkit4: /usr/lib/x86_64-linux-gnu/libQtWebKit.so.4.10.2
If you prefer to use a web browser, go to http://packages.ubuntu.com, search for libQtWebKit.so.4 in "Search the contents of packages" and you will get:
File Packages
/usr/lib/aarch64-linux-gnu/libQtWebKit.so.4 libqtwebkit4 [arm64]
/usr/lib/arm-linux-gnueabihf/libQtWebKit.so.4 libqtwebkit4 [armhf]
/usr/lib/i386-linux-gnu/libQtWebKit.so.4 libqtwebkit4 [i386]
/usr/lib/powerpc-linux-gnu/libQtWebKit.so.4 libqtwebkit4 [powerpc]
/usr/lib/powerpc64le-linux-gnu/libQtWebKit.so.4 libqtwebkit4 [ppc64el]
/usr/lib/s390x-linux-gnu/libQtWebKit.so.4 libqtwebkit4 [s390x]
/usr/lib/x86_64-linux-gnu/libQtWebKit.so.4 libqtwebkit4 [amd64]