The idiomatic expression "run down one's contract" means to use up or exhaust all of the terms and conditions specified in a legal agreement, such as a lease, employment contract, or service agreement. Full definition
It seems the German club would rather a player run down their contract in hope of a late commitment, rather than to sell for a cheap fee. (justarsenal.com)
This money hungry owner would not be so dumb to let them leave for free after running down their contracts and ruining the atmosphere in the dressing room. (justarsenal.com)
You see what he is trying to do in running down the contracts of the players that are in final year? (justarsenal.com)