Can't speak to movies but at this age I loved Star Trek Voyager. Lots of episodic episodes facing real issues/moral decisions.. insightful.
Depending on the 11-year-old, you might be able to make a case for Seth Macfarlane's The Orville, which can be a bit more hit-and-miss, but does have some truly excellent episodes, particularly in Season 3.
The newer Star Trek series coming out are probably too gritty if the parent is worried about age-appropriateness (I believe Picard has a TV-MA rating?) and unless you really like The Original Series, it's pretty noticeably a product of its age and I personally had trouble staying engaged by it when I was that age.