We study an indefinitely repeated Tullock contest in which the stage-game winner gains an incumbency advantage in the next stage-game. The incumbent's advantage allows the incumbent to carry over a proportion of their expenditure in the previous contest to the next contest. Theoretically, this advantage is not predicted to have a large impact on total expenditure. However, in a controlled laboratory experiment, we find the incumbency advantage increases total expenditure by a significant amount. Further, we find that carryover has a discouraging effect on challengers while encouraging incumbents react in a retaliatory manner.