That depends on what tests you are running. In any significant projects you need a test suite so large that you wouldn't run all the tests before pushing to CI - instead you are the targeted tests that test the area of code you changed, but there are more "integration tests" that go through you code and thus could break, but you don't actually run.

You can also run some static analysis that is too long to run locally every time, but once in a while it will point out "this code pattern is legal buy is almost always a bug"

It is also possible to do some formal analysis of code on CI that you wouldn't always run locally - I'm not an expert on these.