How to remove new icon from dock

Control-click it and choose Quit. If it remains, use Remove from Dock under Options, or drag it out.

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That is the Terminal app and with the dot below it that means it is currently open. Open apps will appear in the dock, so tap it and quit the app. The right portion of the Dock will display Recently Used apps, so you may see it remain there until other recently used apps replace it. If you don't want Recently Used applications to appear in the Dock, then you can go to the Mac System Settings and uncheck that option for the Dock.