Her latest book has engendered a lot of contraversy.
Is this statement having correct verb tense?
Sure, "Her latest book has engendered a lot of controversy." is a good sentence. The tense suggests that the controversy started in the past and continues through the present, so the book still engenders controversy.
Not to be too picky, but if you're wondering about tenses, your question should be in the simple present, "Does this statement have the correct verb tense?"
Hope that helps!