“Six months after graduating, I signed with a gallery in my hometown. I’ve sold a good deal over the past 2 years, but as I continue to make new work, I feel as though I may have outgrown this gallery (and this city). I have a new body of work that I would like to exhibit elsewhere. Advice on how to make this happen?”
First of all, this is a good “problem” to have, as the majority of the time it is the artist being rejected by the gallery. The best approach in your scenario is to be gracious, polite and honest. Keep it short and sweet. Thank the dealer for their support of your work early in your career, and then simply explain that your career is growing and that you would like to move on to other venues. Don’t feel obligated to get into too many details on why you’ve made this decision. The more simple your response is, the better. Remember, galleries (especially smaller, less established ones) have likely dealt with artists leaving them before, and they will probably understand. I would also recommend doing this over the phone or in person if you can. I think email is too impersonal for this kind of conversation and might come across as curt.
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Clara Lieu 
I agree, e-mail is too impersonal! It can come across as unintentionally rude/cold/etc., which is not a good note on which to end.
Because I don’t like to “burn a bridge,” I often say I need the work elsewhere. That way, if they want me back, or I want them back, we still have an open door.