Bridle of Chivalry.
An oddity even among the Noble Phantasms, it is a bridle and whip paired as a set. As you’d expect, it has no effect without a mount to use it on.
It is a rank A+ Noble Phantasm, and has extraordinary offensive and defensive capabilities.
When Pegasus is directed by Bellerophon, its limiters are removed and all of its ability scores increase by one rank. On top of that, its defensive power is improved by several times due to the protection of its colossal magical energy.
If Saber’s Excalibur is a golden flare, then you could say that Rider is a white comet.
Oh! This is just a digression, but the name of the young man who tamed and rode Pegasus in Greek mythology was—you guessed it—Bellerophon.

Fate/side material: Fate Encyclopedia