I'm afraid there is no such option. An image that you license can be licensed by other Stock users as well. Once licensed the image remains with you even after you have canceled your subscription.
Let us know if you have any other questions around this.
is there a possibility on Adobe Stock to buy a photo which only i can use? So no one else can buy it afterwards?
That's not how stock works. Stock means to take pre-made (shot) assets and use them in your creative projects. If you want exclusive rights, ask a creator (photographer) to organize the shoots you need.
Stock costs 50$-, the photographer/stylist/model will cost 1000$+. But you will get exclusive rights.