I do not believe that there is a way to clear your past queries from the Results display window without exiting Stata all together.
We will talk more in Lab 2 about how to keep your different projects organized with "do" and "log/smcl" files. With these files, you will be able to keep your coding, notes, and Stata output for each project separate, which will be helpful when you want to go back and make changes (e.g. add/delete commands) and to share your work with others.