It’s the issue no government contracts lawyer wants to discuss, the matter they wish would go away.

Yet some government contracts practice groups are being forced to spend more time than ever trying to prevent, or at least mitigate, conflicts between clients.

Client conflicts are one of the most sensitive issues facing law firms and some of their biggest contracting clients, such as Boeing, General Dynamics and Northrop Grumman. They go to the heart of law firm-client relationships—and how important it is to keep existing clients happy while also pursuing new work.

Client conflicts are on the rise because of...