Your senior leader is the Senior Instigator of what goes on with evangelism and outreach at your church. He may not be naturally gifted at evangelism, but he can learn to reach out just the same. At the bottom of it, all this is more about one’s willingness to reach out. God will provide all the desire you need.
If you are blessed you might have one or more true Evangelists present in your congregation—those who can stir up evangelism. Those people are able to raise the belief in a large group of people that it is doable to reach out to the surrounding community.
Pray for your senior leader.