From 1697-1708 Arda Tuluva was embroiled in a Civil War. Prior to that the nation was gripped by famine, natural disasters, and insurrections. In 1697 the Empire plummeted into a civil war, a large faction from the army and noble families had declared that the Vildimë Dynasty had lost the Mandate of Heaven and supported the minor noble house Sarëar.
After 11 year of fighting the last stronghold from the Vildimë Dynasty surrendered and the Mandate of Heaven officially transferred to the newly created Tercenë Dynasty in 1708. This period following was one typical of a Dynastic Cycle, Noble Families and ministers that were loyal to the old Dynasty during the war were purged, executed, forced into suicide, or exiled. As well as, the new Dynasty's consolidation on power and rebuilding the war-torn infrastructure.
Therefore, Arda Tuluva wouldn't have the power to defeat these pirates alone. Also, they would not want trade to be disrupted during the first decades of their reign.
A possibility of where the Pirate Fleet came from. When the Empire plunged into war the Admiral of the Vildimë Fleet (who was never the most loyal or honorable man, as his post was an appointment from corruption) saw an excellent opportunity to take advantage of the situation. Since the war began no gold was coming from the capital, how was he to pay his men? There was little food from the famines, how was he to feed his men? Piracy. The Vildimë empress was too busy fighting to keep her throne and so he and his ships set sail and found some small islands to set up base. They raided, pillaged, and continued to recruit and build up a power base.
A thought I had, as then there is a reason to how the Pirates seemingly came out of nowhere. Also, Arda Tuluva, to save face, would have said the rebels burned their fleet a port instead of admitting their officers were mutineers and dishonored.