Yes, an oil pump can get clogged. You might have some sludge buildup in your motor which can clog up the screen on your oil pump. The problem is that even if you change your oil, the sludge is still there ready to cause the same problems.
Can you clean oil pump?
How does an oil pump get damaged?
Oil contamination, in the form of gasoline in the oil, metallic wear particles, or any other foreign substance in a vehicle's oil, can, over time, cause an oil pump to fail.
When should you replace your oil pump?
If you're thinking it's weird that you haven't replaced the oil pump yet on your 10-year-old daily driver, don't worry; oil pumps typically last 150,000+ miles or the life of the vehicle, but only if you keep up with the required maintenance.