want to remove existing outlook account and add new one in outlook 365

You need to ask the administrator that maintains your O365 tenant. There is a list of users in their. You need to remove the license from the old employee, create a new employee and assign the license.

I asked this wrong.  Got some new info.  Right now a user is logged into the outlook account with their credentials on a laptop. A new employee is getting this laptop.  I don't want to remove the license of any user.  I want to change the user that is signed into the outlook account on the laptop

and the new user has been assigned his own O365 license?

did your laptop joined a domain or is it standalone? Running Windows 10? If standalone and Windows 10, then from the settings of your computer, click on "Add someone else to this PC" from the Other users dialog to add the new user.

The new user and the old user both have office 365 Business Premium licenses.  It is joined to a domain.  Windows 10 Pro.

if the laptop has joined a domain, while connected to the domain, the user just have to use his network credentials to connect to the computer (no need to "add someone else to this PC").

are your O365 and network AD the same and/or synced? or are you running 2 ADs?

They are not synced.  That is something we are in the stages of changing.  Right now, when I setup a new computer and add the 0365 account, I use the employees email address and password to login the O365 account.

because the 2 AD are not synced, you need to create your new employee in both the O365 tenant and in your domain. In your setup, the 2 ADs don't talk to each other.

I'm sorry.  I must have misunderstood.  We do not have 2 ADs.  Just 1.  When I setup a new computer with o365 I use their email address and password to sign in to outook.  All I need to know how to do is open outlook on the computer and remove the account that is in there and add a different account.  I know how to ADD another account so there are 2 inboxes, but I want to completely get rid of the account there (on the computer, not in O365) and add a different account using email address and password as credentials.  I think I am explaining a simple task and making it confusing.  Sorry.

Very confusing.

But is the new user login in on the laptop with the credentials of the old user?

Usually, a user logs in Windows with his own credentials. Once logged in, he starts Outlook. Because it is a new session in Windows, Outlook will have no mailbox set and will ask for credentials.

Otherwise, in Outlook, under File, you should have a "Add account" button.

OK.  I see the add account button.  If I use add account that will add the new user and then I will have 2 inboxes.  I want the current user to be removed from this computer.  Not sure what I'm asking wrong.

You haven't answered my previous question

How will your NEW user logs on the computer? Usually, a NEW user logs in Windows with his own credentials. Once logged in, he starts Outlook. Because it is a new session in Windows, Outlook will have no mailbox set and will ask for credentials of the NEW user.

So Outlook will not show 2 mailboxes in the session of the NEW user. Outlook has different configuration for each computer logging into their own Windows session.

We are talking 2 different things.  IT at this office changed the login to a different user but the outlook account is still the old employee.  I want to open up outlook and add the new employee using their email address and password.    I know I can ADD the email account in outlook but this will give me 2 inboxes then.  I only wnat 1 for the new employee.  See screenshots.
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create a new profile in outlook: https://www.bemidjistate.edu/offices/its/knowledge-base/create-a-new-profile-in-outlook-2016-windows-10/

ok. will this remove the email account that is in their currently?

or in your current setup where you have 2 mailboxes, right-click on the mailbox you don't want anymore, and delete it