Hormone-based contraceptive methods (such as the oral contraceptive pills, implants, and injectables) are safe for most women who are 35 and older—but if you smoke or have a history of certain health conditions, then there may be risks posed.
If you smoke and take oral contraceptive pills or other contraceptive methods that involve hormones, your health risks increase significantly after 35.
Using contraceptive methods that contain estrogen is highly discouraged; estrogen and smoking interact in the arteries, which increases the risk for heart attack and stroke.
Research shows that the risk increases greatly after the age of 35, perhaps because the risks for a number of health conditions are also greater for women as they age.
If you have other health conditions or medical history such as severe diabetes, hypertension, migraines, and liver or bladder disease, consult your doctor about the possible risks involved. You will be given an appropriate medical feedback and recommended options for effective contraceptive method that will work best for you.
Progestin-only contraceptive methods are usually safer for women over 35. There are pills, implants, and injectables that only contain progestin, but it’s best to consult your doctor or healthcare provider first.
Source:
https://www.everydayhealth.com/sexual-health/over-35-the-best-birth-control-options-for-you.aspx
https://www.singlecare.com/blog/birth-control-for-women-over-35-and-40/
https://www.webmd.com/sex/birth-control/birth-control-40s-50s
https://www.healthgrades.com/right-care/birth-control/birth-control-choices-for-women-35-and-older