Assuming this is a search campaign, you should be able to see if any new competitors are regularly showing for your keywords. I would also investigate if CPCs have changed (or just conversion rate), how your impression share has changed, and how your average position has changed.

If their campaigns are profitable, they will probably continue to run them. Your best bet in the meantime is to optimize your CPC, CTR (helps with CPCs), and conversion rate. You have the history and experience, which should be to your advantage against a new competitor.