Transfer Database

I am transferring my hosting to a new registratar. Thus far I have already downloaded the files (themes, plugins, etc.) I need.

Is it possible to transfer my old piwik database to my new hosting account and continue gather stats without interuption or will I need to install a new database? Thanks for your time.

See faq Installation - Analytics Platform - Matomo

Yes. Did that a couple of months ago.

(Assuming mysql)
If you have shell access to your server, just use mysqldump to get a backup of your piwik database.
mysqldump -u USER -pPASSWORD PIWIKDB | gzip > piwik.sql.gz

If you don’t have terminal access, I recommend to use Mysqldumper. I had lots of problems dumping the big piwik tables using phpmyadmin.
http://www.mysqldumper.net/

On your new server you have to import the database and configure piwik to use it the same way you did on your old system.