If you intent to develop your site offline in your localhost , make sure your local server has the same config as the webhosting server that you might use the actual online site.
Make sure both Apache / PHP & MySQL are of same version.
This is the basic check that you need to do before working .
Coming to your question.
When you restore a database , the old database gets deleted & this gets in place on the database server.
But to be on the safe side , delete the database manually & then create the database again & restore the database.
As it would run smoothly.
Hope this helps :-)