Friar Tuck is a companion to Robin Hood in the legends about that character.
Tuck is a common character in modern Robin Hood stories, which depict him as a jovial friar and one of Robin's Merry Men. The figure of Tuck was common in the May Games festivals of England and Scotland during the 15th through 17th centuries. He appears as a character in the fragment of a Robin Hood play from 1475, sometimes called Robin Hood and the Knight or Robin Hood and the Sheriff, and a play for the May games published in 1560 which tells a story similar to Robin Hood and the Curtal Friar. (The oldest surviving copy of this ballad is from the 17th century.) It has often been argued that the character entered the tradition through these folk plays, and that he may have originally been partnered with Maid Marian. His appearance in "Robin Hood and the Sheriff" means that he was already part of the legend around the time when the earliest surviving copies of the Robin Hood ballads were being made.
A friar with Robin's band in the historical period of Richard the Lion-Hearted would have been impossible because the period predates friars in England (but see Eustace the Monk, a medieval outlaw); however, the association of the Robin Hood with Richard I was not made until the 16th century; the early ballad A Gest of Robin Hood names his king as "Edward".
What follows is a story which includes different versions of the legend. He was a former monk of Fountains Abbey (or in some cases, St Mary's Abbey in York, which is also the scene of some other Robin Hood tales) who was expelled by his order because of his lack of respect for authority. Because of this, and in spite of his taste for good food and wine, he became the chaplain of Robin's band. In Howard Pyle's The Merry Adventures of Robin Hood, he was specifically sought out as part of the tale of Alan-a-Dale: Robin has need of a priest who will marry Allan to his sweetheart in defiance of the Bishop of Hereford.