1 usually make inroads in/into/on – An instance of something being encroached on or reduced by something else.
2 A hostile attack; a raid.
Mid 16th century (in inroad (sense 2 of the noun)): from in+ road (from an early use in the sense ‘riding’).
The duke and his trusted henchmen crossed into the neighboring region on the day after their lord died, planning to “offer condolences and support” to the ten-year-old successor. In fact the duke planned a regency through which he might make inroads and assume control of the land.