Final answer:
The missing word (modal) in the provided sentence should be 'need.' The completed sentence informs us that British citizens do not need a visa to travel to the US.
Step-by-step explanation:
The sentence provided is incomplete and requires the appropriate modal verb to accurately convey the necessary information. In the sentence provided by the student, the missing modal verb should be 'need', which is used to express necessity or requirement. So, the complete sentence should read: "British people do not need to get a visa, but there are different rules for different nationalities." This sentence indicates that while British citizens are not required to obtain a visa, other nationalities may have different requirements when travelling to the US.