What the Travellers' Aid Society does In My Traveller Universe
In the Third Imperium the feudal unity of the government makes a sector-spanning entity like the TAS possible. The Imperium is everywhere, so the TAS is everywhere as well. In my TU, there are multiple competing governments, none of which controls all of 'known space'. However, there is an organization that does span the map: the Church.
Why does the Church run the TAS? One of the reasons is right there in the name: Aid. For the Church to offer aid and assistance (the ecclesiastical word is alms) to those who venture across the stars just makes sense. The Church is a community. Parishes live and work together and help those around them. This is called almsgiving, and it is an essential part of what the Church is and does. The TAS takes as its foundation Jesus' parable of the Good Samaritan found in Luke chapter 10 which underscored his teaching to "love your neighbor as yourself".