Yes, but it requires switching screens. When you click your nickname in the top right corner and then click the "Become Spectator" or "Switch to..." button, then you can join in a different role – change a team, switch from a spymaster to an operative, and vice versa. This way, the operators should look elsewhere while the spymaster is typing the clue, so they don't see the grid with colored cards. Once he is ready, he switches to operator and others can look and guess. When they are done with guessing, the operators look elsewhere again and you need to switch to the other team's spymaster and so on.
Also note that when you open the game in more browsers (Chrome, Firefox, Edge, etc. ) or in a private (incognito) window, you can log in under a different nickname in each of them. Then you can simply switch windows based on who's turn it is.