Stuff you do outside battletime need not be based on skills or even as involved with the mechanics as trading, but there are a few main PD-provided chunks of game:
You could (though in Dawn it’s mostly a yeoman thing) go for trading; match people to things, get people what they need when they need it and pick up a little commission on the top. Quite possibly not what you’re after, unless I miss my guess.
There’s the Synod and priesting - bothering people about Virtue, encouraging the nervous and recognising cool people. Dawnish priests are known as troubadours, and often inspire through some sort of performance - but despite the name the brief does say that storytelling or similar is just as valid as singing.
Magic has a couple of (sort of related) areas of game beyond battle magic. There’s supporting the Empire through ritual magic, some of which goes through the Conclave (but you don’t need to worry about that if you don’t want to!) - this includes making the military more awesome and also stuff like trying to find out what’s going on or, if you do get into Conclave stuff regulating use of magic. Then (and in Dawn this one’s pretty big) there’s interacting with Eternals. They can have varying opinions on the Empire - some like us, some are angry, and people can and do attempt to win their boons and turn away their anger. I’ve got into the periphery of that bit myself, and am hoping to go further with it next event - should be a lot of fun!
Then of course there’s sitting around singing songs, meddling in love lives, making friends, challenging people to do things, making enemies… the little social things that can really keep a game running.
Taking a few points of combat and a few points of off-field stuff can work; if you were interested in the magical end of things, you could take Magician, 2 ranks in a lore, a spell for the battlefield (I took Heal) and the other two on something else; that gives you an excuse to hit the battlefield (healing! Am usefuls!) but also some skills to use off.
Other, similar things include taking some priestly skills for inspiring people off the battlefield, then picking up Stay With Me and maybe Chirurgeon and continue to inspire people on the battlefield - so inspiring they KEEP FIGHTING!!! despite awful wounds.