Open the Slack Desktop app and log in using your current password.
Click your the Slack organization name dropdown and select Profile & account.
In the sidebar pane, click the
[•••] triple dots and select Open account settings.
You will be redirected to the Account Settings page on the Slack website. From here, simply click Expand under the Password section and use the form to set a new password.
While you're in here, I also recommend setting up Slack Two-Factor authentication.