No you cannot and will not get fat by eating fat.
Eating fat from food will not make you fat.
Your body will just use the fat you consume for energy so it would get burned off.
Calories are what makes you fat and the more calories you consume the more weight you gain if you don't burn those calories off.
When you have meat fat the fat from the meat is usually hard to chew so I mostly throw that out.
But if you can chew the fat from the meat then it's okay to eat it.
However the meat fat is not very good for your health when eaten too much.
But in moderation it's okay.
Some other types of fat are healthy but some aren't.
But you won't gain anymore weight when eating fat unless you eat a whole lot of it.