Since a civilization advanced enough to be capable of manufacturing a new star would likely have vast material and energy resources at its disposal, it almost certainly wouldn't need to do so.
Many science fiction authors have explored the possible applications of stellar engineering, among them Iain M Banks, Larry Niven and Arthur C. Clarke.
These perfectly synchronized black holes form a Tipler cylinder called the Texagu Resh gravitational anomaly.
In Firefly (TV series), set 500 years in the future, several gas giants are "Helioformed" to create viable suns for the surrounding planets and moons.
This device creates a wormhole between two points in space, allowing a neutron star to be dropped into the planet and ignite stellar nuclear fusion.