This may be bacterial leaf spot, characterized by black or brown spots that appear on the leaves and streaking on the stems of the plant. Bacterial leaf spot occurs when infected soil is splashed onto the leaves of the basil plant. While there is no fix for bacterial leaf spot, you can minimize the damage by making sure that your basil plants have plenty of air circulation and that they are watered in a way so that the bacteria is not splashed onto the leaves. It is also important not to over water the plants, and be sure the soil drains well.
You might consider replacing this plant with a new one. If you choose to use the same pot, as a precaution you’ll want to remove and discard this potting soil and wash the pot with hot, soapy water before using it again.