Hmm, you can, but you must do something in advance. That is correcting your bootloader. Because the latest grub is valid and you plan to remove that OS you will have trouble.
Reboot and choose the older installation to boot in, probably not the one on top in grub. Once booted open a terminal and give the following commands:
sudo grub-install /dev/sdX #( replace the X with the letter of your main HDD, probably sda)
Now it is safe to remove the partition with the new installation and reassign the free space to something else.
After removing the partition you should rerun
to clean the grub from the no longer existent OS.