The developer of Expeditions: Rome has gone out of its way to ensure that there is no time limit on players to conquer territories. Because of this decision, players can explore the map at their leisure. That said, there’s a bit of a catch.
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The lack of a time limit does not mean that the player can just sit around doing nothing. The more the legion is used, the more costly it becomes to upkeep the events and soldiers. It is no coincidence that the developers gave some consequences for players who do not use their legion to conquer more territory.
There are also events that require players to ensure their legions are in certain areas. Every so often, players will receive information about an attack on a specific territory, and if their legion is not in the territory, it will be lost to the enemy. Having pending attacks on the player every now and then makes it seem like there is still an enemy waiting to strike.
For more information on Expeditions: Rome, check out What Commanders should I pick in Expeditions: Rome? and Can you save Gaius Julius Caesar in Expeditions: Rome? on Pro Game Guides.