They seek to reignite the Vektan-Helghast war, but the thing is, they intend to do so when the time is right. Also, it is mentioned that they are in conflict with the Black Hand, due to them threatening the peace treaty. Now as mentioned above, they want to return to war, but they want to decimate the Black Hand because they intend to restart conflicts too quickly. They need, perhaps, a few more years to ready themselves, and when the time is right, take back what was "rightfully theirs"
Alternatively, the Helghast are already prepared for war, and they are allowing, but not truly supporting, the Black Hands' terrorist acts (persumably using them as a scapegoat). The reason being that they want the Vektans to attack them first, so that the Helghast would have something of a moral high ground and would have sort of a sympathetic reason for retaliating.