I doubt that it would be plagiarism per se, as long as the student cites the source. If you cite something properly, it isn't plagiarism. If you quote the work, make it clear that you are quoting. Make it clear that both the ideas and the words come from the cited source.
It might, possibly, be copyright infringement, depending on who has rights to the interview and whether/how it is licensed. You are copying something, even if changing the media and it might be covered or not. One difficulty here is that you might want to copy the thing in whole, rather than just excerpts, for which different rules might apply.
But a professor might still consider it to be academic misconduct, depending on the rules set for the course. The professor might be expecting you to make the effort at transcription, for example. To know the rules, you need to check with the professor.
Note also that the fact that you paid a service for the transcription has nothing to do with plagiarism. The source of the interview would be the issue, not the mechanics of transcription.