Pirates on trade routes are difficult to eradicate, but a powerful navy could clear them from the seas.
Pirates on trade routes are like flies - annoying and almost impossible to eliminate. They always were and probably always will be. Or perhaps some wealthy ruler will invest time and money in creating a navy large enough to achieve Thalassokratia - rule of the seas? Such power will certainly defeat the pirates and allow sea trade to grow and flourish. Perhaps some ruler will do it in the future? Perhaps even you?
Historically, pirates were usually groups of poor people living on the coast who, using small vessels, attacked lone merchant ships sailing along the coast. Most pirate ships were very light, as they were usually hidden from view on land, behind bushes and other vegetation. But under the leadership of powerful men, pirates sometimes gathered together in huge fleets and were able to blockade sea trade, raid coasts, and even storm fortified cities. These fleets often used bigger ships but sheer numbers were their main weapon against a proper navy. Lembos and liburnae are examples of pirate ships that became very popular and were adopted by major navies...