Answer: No, it is not plagiarism.
Plagiarism can be defined as the act of copying another's work, ideas, thoughts, and presenting them as one's own original work without permission.
In academia, plagiarism is considered to be a fraud or an act of lying.
There are different types of plagiarism, they include; direct plagiarism; self plagiarism; mosaic plagiarism and accidental plagiarism.
This example stated above would have been an example of a self plagiarism as self plagiarism can be defined as an act of copying one's own original text without permission from the professor and without including any new ideas.
But the individual obtained permission from the professor, agreed to include new ideas and also cite all sources previously used.