Log out from your current WCL account, at the top right menu click the Log Out button:
Once you’ve logged out, go to warcraftlogs.com/login. Do not use your credentials for your current account and instead click this:
The correct region button there should sign you into the account your battle.net account is linked to.
Once signed into your old account go here: warcraftlogs.com/profile and under your “Battle.net account information” click the blue button to delete it.
Sign out from the old account and now you can sign in to the new one with your credentials and link your battle.net to it.