There are a number of sites that do variations on what you're describing.
The best of them, though it has issues and is far from perfect, is SpeakerMatch.com. Please understand that I am not endorsing the site, and I think it's not very advantageous to speakers, but it does match speakers with opportunities.
I'm not sure your motive in asking the question, but assuming that you are a speaker looking for opportunities, then the key is not in looking for sites like this, but rather to learn how to effectively market what you do so that when a meeting planner is looking for a speaker, your name comes to mind.
I have to disagree with the last poster on how speakers are selected. When a meeting planner is looking for a speaker, they usually know what topic they want, and often even have specific speakers in mind. That is why MOST speaking opportunities are never advertized, and why a site like you describe can compliment a speakers' marketing plan, but can never replace it.
Public speaking is a challenge to promote as third party, connecting them can be pretty simple I think but might require the service (hosting) site to look for events and the match from existing speakers... I say this because events don't typically have a topic or speaker in mind and is often whoever is available for the event, as long as it matches the events focus. So is a matter of matching per se but of promoting them to opportunities.. My opinion.
Speakers Bureaus have generally played this role. There even exists an International Association of Speakers Bureaus (IASB).
You can search for speakers bureaus by country/state here on the IASB website:
The ones I know of are:
Or just google or search on social media #CallForSpeakers or #CallForPresenters
I wrote an entire guide on how to get booked to speak. Bit.ly/GetBookedToSpeak. Let me know if you have questions.