So, if you see a trickle of oil anywhere on the cowling and/or wheel pant, it’s as if a vein or at least a capillary has been opened. Just as you’d never walk around with an open, bleeding wound, you’ll want to investigate and remedy the source of an oil leak in a training airplane.
The color of the leaked oil is a clue. Is it golden brown, as if it just came out of the bottle? It probably did, and it may be the result of some spillage from the person who added a quart before you. End of mystery. Is it dark brown or black? That’s a signal it came from the engine and may warrant some additional investigation.
Some aircraft engines just leak a negligible amount, and it doesn’t create any safety of flight issues. But unless the airplane and engine in question belong to you and you are very familiar with them, don’t hesitate to raise the question with a mechanic or a flight instructor. Oil leaks never get better by themselves, and often get worse. Ignoring an oil leak is not a habit you want to develop.