Yes! The amount you consume should definitely go up to match increasing levels of activity.

If you're an active person and not into doing complicated math, Douglas Kalman, Ph.D., recommends aiming for somewhere around 1 gram per pound.  

Krissy Kendall, Ph.D., says that 0.8 grams per kilogram of body weight is far too low for lifters and pretty much anyone else who exerts themselves regularly.

"Whether you're an endurance runner or a gym rat, you need more than the average amount to support the recovery and repair of your muscles. In fact, studies overwhelmingly suggest that athletes need more than twice the amount than sedentary people," Krissy Kendall, Ph.D., says in the article "How Much Protein Should You Consume Every Day?"

In a position statement, the International Society of Sports Nutrition says an intake of between 1.4-2.0 grams per pound of body weight for active people is "not only safe, but may improve the training adaptations to exercise training." In a joint position statement, the Dietitians of Canada, Academy of Nutrition and Dietetics, and the American College of Sports Medicine recommend that some athletes can benefit from much as 2.3 grams per kilogram of body weight, or around 1 gram per pound of body weight.[3]

"The more intensely you exercise, the more you should aim for the high end of that range," Kendall says.