I want to use image that was licensed as CC by Attribution 4.0 in my application. Is there any requirements about licensing my whole application? Should it be CC-BY 4.0 too, or can I use different license?
You can choose any (or no) license for your application. You just have to attribute the image correctly.
If CC BY 4.0 were a copyleft license, you would have to license your application under this (or a compatible) license, too. But CC BY 4.0 isn’t a copyleft license. Creative Common’s copyleft licenses all have "SA" (which stands for "ShareAlike") in their name (e.g., CC BY-SA 4.0).