The answer will vary depending on the individual company and its business. If a contract covers ongoing supply and the amount and price are fixed, it might be Operations that takes the lead in the contract management, fulling the deliverables on schedule and notifying AR when action (e.g., billing) is required. In other cases, it might be a situation in which deliverables and price are not fixed, and sales must manage the ongoing relationship. In other cases, the deliverables might be set and billing is once a year (as in an automatic renewal), and there is no need for sales intervention, so AR can drive it.
The AR department should focus on what it does best—extending credit, billing timely and bringing in cash. If the main requirements around the contract are billing, collections, and dispute resolution, it should probably be handled by the AR department.
However, the sales department might have a part in maintaining an account. The sales department often acts as the face of your company and generally has a good relationship with the customer. In some businesses this relationship is maintained throughout the life of the contract as the primary customer service component in order to increase the chance renewal. Of course, your model may be different.
In any case, ideally the departments will work collaboratively. The sales department can use their relationship with the customer to help collect on outstanding invoices. The AR department can inform sales of payment behavior that may indicate an eventual non-renewal or lost account.
For more on how sales and AR can work together to manage customer accounts, see Sales and Accounts Receivable: A Symbiotic Relationship.