How to finish all fetch before executing next function in React?

Your code mixes continuation callbacks and Promises. You’ll find it easier to reason about it you use one approach for async flow control. Let’s use Promises, because fetch uses them.

// Refactor getStudents and getScores to return  Promise for their response bodies
function getStudents(){
  return fetch(`api/students`, {
    headers: {
      'Content-Type': 'application/json',
      'Accept': 'application/json'
    }
  }).then((response) => response.json())
};

function getScores(){
  return fetch(`api/scores`, {
    headers: {
      'Content-Type': 'application/json',
      'Accept': 'application/json'
    }
  }).then((response) => response.json())
};

// Request both students and scores in parallel and return a Promise for both values.
// `Promise.all` returns a new Promise that resolves when all of its arguments resolve.
function getStudentsAndScores(){
  return Promise.all([getStudents(), getScores()])
}

// When this Promise resolves, both values will be available.
getStudentsAndScores()
  .then(([students, scores]) => {
    // both have loaded!
    console.log(students, scores);
  })

As well as being simpler, this approach is more efficient because it makes both requests at the same time; your approach waited until the students were fetched before fetching the scores.

See Promise.all on MDN