Usually an arbitration clause in a contract applies to that contract and survives termination of the contract. So, if you have a dispute with Contract A and the arbitration provision specifies it survives termination, then you'd have to handle the dispute under Contract A's arbitration provision. Since there is no arbitration provision in Contract B, any dispute in Contract B would be handled in court. However, given the cost of going to court, if there is no arbitration provision you realistically don't have any remedy except small claims court. Few attorneys are willing to take a case unless the expected damages are over $50,000 or you agree to pay their hourly rate and deposit a retainer of $10,000.
Answered on Sep 18th, 2017 at 11:32 PM