Login as admin and lick "License / Updates" and on the bottom of that page click "Update DirectAdmin". You should have version v1.20.2 as of this writing?
This should update exim if not you can ssh into your box, as root
#cd /usr/local/directadmin/scripts/ Checking you have the latest exim.sh file if you see the second line you are all set
# grep da_exim-4.24-1.tgz exim.sh
/usr/sbin/pkg_add -f da_exim-4.24-1.tgz