If it's a repair to something structural, simple glue won't be strong enough. The strength comes from the fibres, and if they're broken, you have a very weak spot.
In the general case, which glue to choose often depends on the characteristics not just of the material but the stresses on the join, even once you've identified a class of glues that bond well to the material.
If we consider a non-safety-critical carbon-fibre accessory, so not aerobars, but a bottle cage or a Tailfin pannier rack, the best thing is likely to be epoxy, and a slow-setting one with the parts held together by a jig while it cures. Even then, if it's carrying a load, just gluing the break shut is unlikely to be enough - but you imply you've already thought of reinforcing or building up the join.
On bike frames or even worse, forks, forget it.