Yes, there are clinical trials set up for veterans. The U.S. Department of Veterans Affairs explains how to search for them using ClinicalTrials.gov.
The most important term to include in your search is "veterans" in the "Other Terms" box of the search function. For more information about how to search on ClinicalTrials.gov, visit this page.
If you find a clinical trial and want to volunteer, have a conversation with your doctor or other healthcare professional. They will help you confirm that you can or should participate. They will also tell you the risks and potential benefits of participating.