You can get cervical cancer after a hysterectomy if the cervix remains in place.
If the hysterectomy is a partial one that does not remove the cervix, there is indeed a risk of a woman still getting cervical cancer. 
The Pap Smear
Through the end of World War II, cervical cancer was a major cause of death among U.S. women of child-bearing age. But the introduction of the pap smear has allowed the rate of death from this disease to be cut by more than 60%. 
Along with full and partial hysterectomies, other methods used to combat the early -onset of cervical cancer include the less invasive procedures of cryosurgery, laser surgery, and loop electrosurgical excision procedure (LEEP). 
Cervical cancer now ranks 14th on the list of cancers most frequently affecting women. However, on a global scale, because of the lack in many areas of proper pap smear and other screening procedures, the incidence of cervical cancer is much higher. Four out of five cases worldwide occur in developing nations, fueling the diseases rank as second female cancer on a global scale and third cause of women cancer-related deaths. 
Women who are stricken after a partial hysterectomy with cervical cancer may also be subject to vulvar cancer. This is because the same types of human papilloma virus (HPV) warts that can cause cervical cancer also occur in many cases of vulvar cancer. Smoking is another leading cause of both cervical and vulvar cancer. 
Can You Prevent Cervical Cancer?
In most cases, the HPV virus that causes cervical cancer is spread through sexual contact, so the best line of defense against developing it is to abstain from sex or at the very least employ safe sexual practices by always using a condom. If you are sexually active, regular pap smears are your next line of defense against developing cervical cancer. A pap smear can detect any abnormal cell changes occurring in the cervix before they develop into cancer and can be treated accordingly.  Women are advised to get their first one three years after beginning to have sexual relations or by the age of twenty-one, and to continue submitting to one on a yearly basis after that. 
Smoking is another risk factor in developing cervical cancer. Women who smoke are twice as likely to develop cervical cancer than those who do not. Additional risk factors include the prolonged use of birth control pills, chlamydia infections, poor diets, and young age of first pregnancy or more than three full-term pregnancies.
A number of vaccines, including Gardasil and Cervarix, have been shown to reduce the occurrence of the HPVs that lead to either form of cancer.