How to reset or clear a spy in Jest?

Thanks to @sdgluck for the answer, though I would like to add to this answer that in my case, I wanted a clear state after each tests since I have multiple tests with same spy. So instead of calling the mockClear() in previous test(s), I moved it into the afterEach() (or you can use it with beforeEach) like so:

afterEach(() => {    
  jest.clearAllMocks();
});

And finally, my tests are working like they should without the spy being called from previous test. You can also read their documentation for it

Option 2

If you wish to do it from a global level, you could also updated your jest.config.js (or from package.json)

module.exports = {
  clearMocks: true,
  // ...
}

You can read Jest documentation about it

Jest spies have the same API as mocks. The documentation for mocks is here and specifies a method mockClear which:

Resets all information stored in the mockFn.mock.calls and mockFn.mock.instances arrays.

Often this is useful when you want to clean up a mock's usage data between two assertions.

(emphasis my own)

So we can use mockClear to "reset" a spy. Using your example:

const methods = {
  run: () => {}
}

const spy = jest.spyOn(methods, 'run')

describe('spy', () => {
  it('runs method', () => {
    methods.run()
    expect(spy).toHaveBeenCalled() //=> true
    /* clean up the spy so future assertions
       are unaffected by invocations of the method
       in this test */
    spy.mockClear()
  })

  it('does not run method', () => {
    expect(spy).not.toHaveBeenCalled() //=> true
  })
})

Here is an example in CodeSandbox.