Create a filter selecting the people.
Then do an Export selecting the Gramps XML family tree, NO MEDIA
In the Export Options you put in the Person Filter you created, and for the Reference Filter, change it to Do not include records not linked to a selected person. This will create an export file with the people and just their events, places, sources, citations, etc. You then import this file into your new tree.
If you WANT to transfer your complete Place or Source records leave the Reference Filter to Select All. You can add a filter for just the Notes to pare that list down but it may just be easier to import this file into an empty tree and then use Remove Unused Objects to remove unneeded Notes, Citations, etc. You may need to run this a few times. A note attached to a Citation will not become ready to remove until the citation is deleted first.
If you want any media files stored in a different media folder than their original family tree, then do the Gramps export with media. When you import this file into the new tree, Gramps will extract the selected media files into a folder it will create at
c:\users\%you% (Win10) which you can then move to a better accessible location. You just have to set the new media path for the new tree in Preferences. Or do a hand move of any relevant media files using your OS. You would still need to set the new tree’s media path.