Turkish Airlines Pet Reservation Policy
If you want to bring pet on the Turkish Airline then you must know the pet policy before reservations. Call at +1-888-566-5066 or read this article.

You'll pay the pet fee over the phone, when you add her to her reservation. ... The airline does keep an in-cabin pet listing, so once your pet is added to your reservation, she's getting on board with you. You'll pay the pet fee at the airport.

https://www.one-stophub.com/blog/turkish-air-pet-policy-us