The wiki doesn't list alternative ways to gain honour, as far as I can tell.
So my question is, how do I gain honour as a Priest, because I obviously can't participate in battles, which is the only effective way I know.
Thanks in advance.
Courtiers gain hon/pres by doing bureaucratic work.
Warriors gain it by, as you said, battling.
I have played several Priest characters and haven't noticed gaining hon/pres for preaching. Have played Diplomats as well, but didn't notice any hon/pres when doing diplomacy actions. However, I didn't really pay much attention, so it might have gained and I just didn't notice.