Correct spelling, explanation: considering the history of the language, the word career came into English from French as carriere. But it originated in Latin as carrus which meant a car or chariot. However, in Modern English, the second r does not occur, which shows that it is spelled as career. The learners of English can confuse the word with carrier referring to a device by which something is conveyed, as we can see, it is an entirely different word. To sum up, career is correct, whereas carreer not correct.

Definition of career:
noun/verb, the word used for education, training, and work experience which help you develop your skills and earn more money,
John left his recent job to pursue an acting career.
Although he has already begun his campaign, he insists he doesn’t want to be a career politician.
Kate was hoping for a career in teaching work.

Phrases with career:
career-minded – very ambitious, motivated, for her or his job is the most important thing in life,
When I met him he was very career-minded.
a career path – the way you progress and achieve your job goals,
She wrote an article about the strengths and weaknesses of a career path for athletes.

Incorrect spelling, explanation: career is a noun derived from Latin as carrus with double r but, over time, this consonant became single. Nowadays the word is used as career, however, the form carreer is a common mistake due to other languages, for example in French it is carriere, in Spanish carrera, which shows that in most languages the consonant r remains double. But in Polish, for instance, it is the same as in English kariera with one r. All things considered, solely career is correct, carreer is errorful.

Incorrect spelling

Incorrect spelling

Incorrect spelling