The simple answer is "nothing but wait". And there's nothing that we (or you) can do about it.
Google is constantly searching through websites and indexing content. Once indexed by Google, it's displayed by order of "relevancy", meaning your old event has probably seen more traffic than your recently listed event. Eventually, the new one should supersede the older one as it becomes more relevant to Google's users.
Removing your old listing does not make it disappear from Google's search results as they've indexed it in their system and will continue to display the link to it. In fact, it makes it worse for you as a deleted Eventfinda event page will produce a 404 Not Found dead page when someone clicks on it. At least if someone clicks through to your old event listing, some of that information is still relevant and your new event is very likely to be displayed next to it in the "were you looking for" section.
Google can’t be managed, manipulated, controlled, cajoled or influenced in any way. It’s a mix of science and the black arts. Take heart knowing that they’re consistent about the relevancy algorithms and new should eventually triumph over old.