Don't avoid a conflict between team members, by pretending it doesn't exist. Take action before it gets out of hand. Don't tolerate bullying, harassment or humiliation. Always give both parties the opportunity to voice their ideas and concerns or it is likely to cause resentment and demotivation. Be aware of the stress you and your team work under.
Excessive stress can cause decreased productivity, decreased profits and decreased health.
Stress can be self-induced and you can reduce it if you understand its origins and take positive action. Help the team to grow. As a team leader, your role will change as your team grows. Adjust your leadership approach and style to suit the team's needs. Remember also that people at different stages in their careers need different kinds of support and direction.