Question is about a gynaecologist who sees patients in her private clinic and takes care of them throughout pregnancy then refer them to a hospital for delivery in turn she gets paid for every patient she refers for delivery from the hospital is this incentive halal or haram, she does not conduct the delivery herself.
This is a form of marketing. Marketing is not basically Haram but there is recommended in Islam that treating with fairness (انصاف) with customers in business. And also it is Mustahab if an owner of a business has earned enough profit during a business say sell to customers at rest of day without profit.
If the hospital she market for it is not a valuable hospital according to its service price so it can be considered without fairness to refer patients to there.
Fairness is recommended in Quran and many different Hadith.
O you who have believed, be persistently standing firm in justice, witnesses for Allah, even if it be against yourselves or parents and relatives. Whether one is rich or poor, Allah is more worthy of both. So follow not [personal] inclination, lest you not be just. And if you distort [your testimony] or refuse [to give it], then indeed Allah is ever, with what you do, Acquainted. http://tanzil.net/#4:135
Messenger of Allah Muhammad SAWW said:
Who has sympathy with poor people and treat with fairness with people is a real believer.
Imam Sadiq a.s. said:
The best of deeds are three: having fairness about people so that you prefer for them what you prefer for yourself. helping your brothers and reminding Allah in every situation.
Another point is that a Muslim should not receive one work two times. if the finding a suitable hospital is among the paid services of the gynaecologist so she is hired to do this job for patient as well as she can and receiving a money from hospital is not permitted unless with permission of patient.