Agents invest a lot of time in reading queries, samples (often called partials), and full manuscripts as they consider whether they want to extend an offer of representation. Having an exclusive lets an agent know she’s the only one considering the work, and that another agent can’t snatch it up before she does. You can grant this request or deny it.
If you grant an exclusive on a full manuscript, you may have query letters out to other agents, but should they ask to see the manuscript, you’ll have to hold off until you hear back from the agent with the exclusive. If the request comes after you’ve already sent manuscripts out to other agents, you can’t grant an exclusive. But you can let the agent know the situation instead of giving a flat out denial of the request.
Giving an exclusive does have the potential to slow things down and it might put off other agents who are interested in seeing more, only to find out they have to wait for it. But granting an exclusive also lets the agent know you’re serious about her representation. If you don’t grant the exclusive, you risk alienating the agent who asked for it in the first place, but you keep more options open down the line. There’s no right or wrong decision. Weigh how invested you are in this particular agent. And if you do choose to grant an exclusive, make sure to agree to a time limit so your manuscript isn’t tied up endlessly. A month is common.
Be honest with potential agents and don’t be afraid to ask questions if you’re not clear about a request or the terms of an agreement. This will be an important litmus test for how well you’ll work together, which can help you make a decision should you get the offer.