My old ICloud id won’t delete on my MacBook Pro

how can I delete my old iCloud id? I tried to deleting it manually on system preferences. This is when I bought my MB pro back in late 2011. It. Gave me a id that I wasn’t familiar, nor did not know how to manage ICloud. I tried to sign out, but it just loads forever. When I log in in my new Apple ID, it says it’s not the primary id account. Therefore I cannot get into my iCloud.