In Iraq, the federal government and the authorities in the Kurdistan region are locked in a serious and multipronged dispute over the country’s oil and natural gas resources. The drama is playing out both in the courtroom and via attacks on sites associated with the energy industry.

The dispute has the potential to bring Iraqi Kurdistan’s ruling parties—the Kurdistan Democratic Party (KDP) and the rival Patriotic Union of Kurdistan (PUK)—closer together. But it could also drive them further apart, with the PUK developing a separate relationship with Baghdad...