Pretty much the only (semi-canon) mention was a noodle-incident involving an arms merchant, seen in a deleted scene from DS9: The Die is Cast
TAIN: (thinks) Dukat... ?
GARAK: He's the son of the late Justice Procal.
TAIN: Oh, yes... the business with the arms merchant.
I take it, you'd like to have him eliminated...
Moving further down the canon, Procal Dukat appears in several EU novels including A Stitch in Time. We learn that he was involved in a clandestine "brotherhood" of hard-line conservative Cardassians committed to returning Cardassia Prime to its former glories by systematically attacking the other Alpha Quadrant superpowers and by dominating and enslaving less-developed civilisations within its sphere of influence. Enabran Tain, as part of the supposedly liberal faction was one of those considered by the Brotherhood to be too soft and was scheduled for (ahem) replacement. Tain got there first and had his protegé, Elim Garak, drug Dukat's father (Ziyal's grandfather) and interrogate him. He gave up the existence of the Brotherhood but none of its names and was interrogated to death shortly afterwards.
“Did you go to Romulus?” he asked.
“Yes, I did. With Barkan,” I added.
“He’s good. He’s good, son,” the old man nodded. “But watch him. He’s like his father. If a better deal can be made. . . .” I modulated higher. He was seized by a spasm and his face contorted into a rictus. “That’s what they look like!” he screamed. “That’s what they really look like when you strip away. . . .” His breath ran out and he began to choke in an attempt to refill his lungs. I chose not to modulate down. “We have to . . . kill them. Carriers . . . they carry the disease. Every one of them. Surround the Assembly . . . let everyone watch so they never forget. Ghemor . . . Lang . . . the guls who stand with them . . . especially the traitors!” Dukat was energized and tried to rise as if he were exhorting his troops. The frustration of not being able to poured into his words.
“The Brotherhood has to move now! The families must take their rightful place. Support the Directorate or die. And no exile! Exile is just deferred treachery. Those who were meant to rule must rule. End these negotiations with the Federation. Use the Romulans to drive the wedge! What did they say?” he suddenly asked me. “Will they move with us against the Klingons?”
Obviously this conflicts slightly with the description from the deleted scene, but this is pretty common when dealing with such a peripheral character. No explanation is given for how Major Kira knows about it.