Yes, it is possible for someone to have high level of IQ and high level of EQ.
Although, IQ and EQ are probably not correlated, neither are the two traits mutually incompatible.
People with high IQ are able to perform complex tasks that they have never been shown or taught how to do. They enjoy handling challenges.
People with EQ have a great understanding of emotions and they often use this to their advantage. It is possible for some one to be intellectual smart and at the same be emotionally smart.
Emotional intelligence is defined by our ability to identify, understand, utilize and manage our emotions. It provides us with tools to interact with society. IQ is your cognitive skills demonstrated through learning concepts. It is possible for a person to have both, which can help with academic achievement and scholastic and occupational success.
Both can increase your leadership potential, and improve the quality of your relationships, especially emotional intelligence. Having both can enhance the quality of your professional life. Most people in leadership roles have both. Having both can also help with motivation, procrastination, and perseverance.