The Leader must provide some expectations for the team in much the same way as individuals need clear expectations to perform. A team vision and mission is fine but it is more important for team members to have a set of ground rules and some collective goals (objective and target) around which they can measure their performance.
Individuals within the team need to be motivated. This in itself is not a collective action but demotivated individuals will detract from a good team spirit. If there are tensions between team members don't bury you head in the sand hope they will go away - address there issues proactively.
You have responsibility to ensure that each team member is contributing to the team's performance and that any underperformance is addressed swiftly. Carrying unwilling passengers can be most damaging to morale within the team and , worse still, left unattended will cause long lasting resentment.
Team members have to understand the benefit of collaborating with each other rather than competing. There is no place for one-upmanship in high performing team and, in this respect, individual goals and reward systems need to work in favor of collaboration.
Something Extra :
Team members should be encouraged to do things as a team. This could be anything from socializing as a team to having their own fantasy football mini - league or book club. Most importantly though, this must come from the team members and not the team leader. You can only support the process by perhaps making the budget available or joining in.
Team away days :
A well-structured, well-run team away day can be a really powerful medium for accelerating team spirit. A shared experience is one of the most powerful ways to bring a group of people together and regard themselves as being part of a team. Typically, an away day should have a combination of serious business and fun activities.