King Henry VII was the first Tudor King of England, and the father of the series' main character King Henry VIII. He never appears (having been dead years prior to the show's timeline), but he is mentioned several times.
In series one, King Henry VII is briefly mentioned by his son, the present King Henry. He is evaluating his marriage with Catherine of Aragon. He says that once Catherine's first husband (Henry VII's son and Henry VIII's brother) Prince Arthur died, Henry VII arranged for the then Prince Henry to marry Catherine so he would not lose her dowry.
When the North rises in rebellion in 3x01, King Henry VIII reminisces about the Cornish rebellion against his father in 1497.