It really does start with the right person and this is often best known by watching people as they experience serving opportunities and how they handle smaller responsibilities. You are looking for a person with the right character, the right temperament, the right social skills, and the right administrative skills. Know what you are looking for and keep lists of potential team leaders.
We can’t stress this enough: it’s so important to define the responsibilities of your team leader… what do you expect of them, what can their team expect of them, and what should they expect from themselves? You may also clarify what’s not expected of them.
Never miss the opportunity to be looking for future leaders and training one or two people on every trip. You can make this as formal as you'd like, but also be training new leaders in the environment of known and trusted team leaders. Give these leaders in training an opportunity to lead and to fail. It’s much better to provide these micro leadership experiences before you allow them to lead their own trip.
Don’t expect your team leaders to just magically appear. This is a skill and it takes training. Consider a team leader training program where you help equip them, clarify expectations, help them navigate team preparation and team conflict resolution, and equip them with the tools to lead well. Ask former team leaders what makes it a success and what tools or training they wish they would have had.