What is Run up ?
Run up is (verb) 1. to go up something quickly on foot She ran up the stairs carrying a thermometer. The runners have to run up the mountain and back again. 2. to run up to someone to come closer to someone quickly on foot He ran up to the policeman and asked him to call an ambulance. 3. to make debts go up quickly The business was running up debts of thousands of pounds each week. 4. to sew something quickly I can run up a cushion cover in less than an hour.
source: Easier English, Student Dictionary Upper Intermediate Level