Correct spelling, explanation: career is a word borrowed from French carriere. In English, the word became adjusted to the standards, so the ie became ee, and the silent e at the end was dropped. The double r also became redundant due to the pronunciation.

Definition of career:
1. Something a person does for a living; a job, usually with good prospects for the future
He was always very ambitious, so he just had to pursue a career in the medical field.
She seemed destined for a career as a nurse just like her mother.

Incorrect spelling, explanation: based on the pronunciation, both ee and ea can be read as long i sound, however in the case of carrear, the spelling can’t be considered correct, as the origin of the word is in French carriere. In the process of changing vowels, ie became the double e, which is much more typical than changing to ea.

Incorrect spelling

Incorrect spelling

Incorrect spelling