The term 'Run a Tab, Say' is a job description for someone who is responsible for keeping track of a customer's tab at a bar or restaurant. This person must keep track of what the customer has ordered and how much they owe for their purchases. The crossword solution for this term is 'OWE', which is an abbreviation for the verb 'owe'. This verb means to be indebted to someone for something, such as money or goods. Therefore, the job description 'Run a Tab, Say' can be summarized as someone who is responsible for keeping track of a customer's debt at a bar or restaurant.