I assume your questions is about importing the DB again in MySQL?
Are you still able to export the database from your not working site? Than you could do this (source):
mysqldump --add-drop-table -u user -p > dumpfile.sql
And import it again on your new site with this command:
mysql -u user -p < dumpfile.sql
You won't get the error about already existing tables.
If you can't reach the old database anymore or not able to export, drop the current database first on your new site (make sure you made a backup).
DROP DATABASE databasename
CREATE DATABASE databasename
You can also drop all tables instead of dropping the database. You can use this script: https://www.cyberciti.biz/faq/how-do-i-empty-mysql-database/
Or my preferred method is using PHPMyAdmin to drop all tables.
Then re-import with:
mysql -u user -p < dumpfile.sql