Can a real refrigerator have higher COP than the COP of the Carnot refrigerator?

Answer: NO

No

Explanation:

As we know that Carnot refrigerator is an ideal refrigerator in which all processes are reversible and COP of refrigerator depends only on temperature limit of evaporator and condenser.

On the other hand a real refrigerator consist irreversibility that is why the COP of real refrigerator is less that Carnot refrigerator.

So we can say that COP of Carnot refrigerator is always more that COP of real refrigerator.