Henry VII's power in Ireland only extended as far as an area called The Pale; the rest of Ireland being ruled by the barons who settled there during the twelfth century (the Anglo-Norman period).
The most dominant of these leaders was the Earl of Kildare, who had been Lord Deputy of Ireland since 1477. However, he had supported Lambert Simnel, crowning him in 1486 as King of Ireland. With these Yorkist sympathies, he also showed support for the pretender, Perkin Warbeck. So, he had to go.
Henry VII instead made his own son, the four-year-old Prince Henry, Lieutenant of Ireland and appointed Edward Poynings as his deputy.
It was in this year, 1495, that Poynings established Poyning's Law which decreed that Ireland was unable to pass any law without English approval and also attempted to establish English law in Ireland.
To begin with, Poynings used force and bribery and managed to establish some English authority but this proved to be quite expensive for Henry VII.
By 1486, Kildare had decided he no longer wished to support the Yorkist cause and offered up his loyalty in return for his former position. Once re-established, he was able to bring a lot of the Irish chieftains on side and by 1500 they had something resembling peace. Kildare was also able to reestablish his family's fortune.
These events are an example of something that Henry VII was excellent at - securing loyalty via second chances. These gambles could have often produced terrible results for him but generally seem to have paid off.
However, it would be these extra chances that would lead to the persistent Warbeck attempting to claim the throne repeatedly over the next few years.