Success is really a team sport, so the more people you have supporting what you want to achieve, the more you will achieve. When people feel a part of something (involved), they will always feel more attached and will often take more action on it as well.
In leading a team, one of the best ways for your people to feel this attachment is to ask for their input. When they see their input into the initiative (their part) , they will always provide stronger support the whole initiative as they want their input to be used and successful.
So, input drives support. Get your people providing more input (becoming more involved) and you will gain more support with your team’s initiatives.