I am assuming that the view that is already in use is of type block.
You can clone the Block using the views admin UI.
1)Go to Structure -> Views
2)Click on the Edit link corresponding to your view
3)Click on the block you are interested in copying and select the option "Clone Block" from the dropdown.
4)A copy of the block gets created. Update the title of the new block , make the necessary changes to the filters etc and save.
oops!Missed out the important piece "
The view should display the events which are currently available in a
From what I understand the multi-site setup is achieved using the Domain Access module. So the drupal instance and the DB are common for all the sites.
In your case you need to make the events content available in the domain where you are creating the view. To do this
1) Go to Structure -> Content Types
2) Click on the edit link corresponding to the Events content type
3) Click on "Domain Access Settings" at the bottom
4) Select the Domain where the events view is going to be added and save.
5) This domain access setting gets applied to all the new events which get added after the change.
6) The existing events might have to be manually updated to make them accessible in the different domain. Go to the edit page of each specific event and update the Domain Access options accordingly.