Answer: runsup

AnswerCrossword Clue
RUNSUPAccumulates
RUNSUPAdds to, as a bar tab
RUNSUPKeeps an open tab
RUNSUPAmasses
RUNSUPAccumulates, as a tab
RUNSUPAdds to, as a bar bill
RUNSUPIncurs