I believe this is not possible, since the tabs are just for better organizing the components/layout of a screen. You can add a custom field to multiple screens, though, by setting the Custom Field properties. This link will tell you how:
Too bad that this is the answer, and it still seems to be the case in Jira cloud in 2019.
I could really use the same feature: I have a very large form with some Master-Detail relations.
E.g. on tab 1 I have a button to select if something is an 'Investigation Required'. On a different tab I want to repeat that value, and add fields 'Investigation Plan', 'Investigation Summary'. This field is only required when 'Investigation Required' = 'true', so the user should not feel compelled to fill these values when not required to. But I still want it optional..
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