There isn't a specific place in Outlook for Android where you can update to a new password, but you can initiate the process as follows:
Exit Outlook and reopen the program. You will then be greeted by the following message:
Enter your new password both under IMAP server incoming e-mail and under SMTP server for outgoing e-mail
Then click on the checkmark at the top right.
Your e-mail account is now ready for use!