I assume, you have installed the kernel manually without a PPA or from the Ubuntu repositories. Therefore you will never get an update and also not, if you remove you 3.x kernel.
To install a supported kernel, follow @Pilot6 answer or search a PPA for a kernel with version 4+.
Or install a kernel via deb packes from here, but you have to repeat this procedure for each new kernel version.
Eg (replace the filenames with you preferred kernel version):
Download the packages
For 64 bit systems
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.0-vivid/linux-headers-4.0.0-040000_4.0.0-040000.201504121935_all.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.0-vivid/linux-headers-4.0.0-040000-generic_4.0.0-040000.201504121935_amd64.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.0-vivid/linux-image-4.0.0-040000-generic_4.0.0-040000.201504121935_amd64.deb
For 32 bit systems
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.0-vivid/linux-headers-4.0.0-040000_4.0.0-040000.201504121935_all.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.0-vivid/linux-headers-4.0.0-040000-generic_4.0.0-040000.201504121935_i386.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.0-vivid/linux-image-4.0.0-040000-generic_4.0.0-040000.201504121935_i386.deb
Install the packages
sudo dpkg -i linux-headers-4.0.0-*.deb linux-image-4.0.0-*.deb
Update grub
sudo update-grub
Reboot your system