Sir Gillium is the Flying Derby Coach of the Royal Preparatory Academy.
When Princess Sofia announces she wants to try out for the team, he, along with the attending princes and princesses, tried to explain that derby-racing was a "princely thing" and not a "princess thing", Sir Gillium apparently worried of Sofia hurting herself.
She didn't take no for an answer however, and Sir Gillium directed her to the last winged horse available, Minimus.
But when the try-out race came, Sir Gillium watched as Sofia, along with her brother, Prince James, managed to win the race together, and he proudly awarded them the Racing Derby jerseys.
He apeared again in The Shy Princess, having brought in Minimus for the art class to paint as the winged horse modeled, and leading him back out once the painting was over. Sir Gillium is not the first Flying Derby coach, as a portrait in Roland's palace shows another, more jolly and older looking man near one of the columns used in the Derby training field. Since this portrait was in Enchancia, there is a Flying Derby team in Enchancia that Sofia wanted to be in when she was young and Sir Gilliam is British, Flying Derby may very likely hail from Enchancia, though the flying horses likely aren't native to the kingdom.