If you don’t have a separate /tmp partition defined, you’re likely using cPanel’s tmpDSK method of setting up /tmp. By default, this “partition” is 512M in size, and for many that’s enough, but others need a larger /tmp.
So first, let’s edit /scripts/securetmp, and modify $tmpdsksize to increase the number of bytes this partition should have.

Once you’ve set the value for $tmpdsksize, save the file, and let’s see what processes are using /tmp.
lsof /tmp
Likely, you’ll see a few MySQL and Apache processes. Now we’ll stop these processes (and any others using /tmp) so that we can unmount it.
service httpd stop
service mysql stop
Then umount /tmp and /var/tmp:
umount -l /tmp
umount -l /var/tmp
Then remove the old tmpDSK:
rm -fv /usr/tmpDSK
Then create your new /tmp:
/scripts/securetmp