[q="peterfinarovsky"]If you're asking whether a naval ship moves to hunt in an adjacent sea zone without an event, the answer is no.
With my group, I play this differently.
If there is a pirate captain, naval ship moves every time, towards that captain's ship, if he/she is 1 or 2 spaces from it. That way, you can never be too safe. That pirate must stay alert, and carefully chose his actions.
We also agreed on buying a d8 compass die, so that naval ships move around all the time.