Little Richard had "retired" from rock'n'roll while on tour in Australia in October 1957 and had made a "comeback" while touring the UK in October 1962. While he had spend the years in between recording and performing gospel his backing band the Upsetters had gone on to work as solo artists and backing other performers thus Little Richard needed to put together a new band.
It seems that at no time during the 60s was the line-up of the band particularily steady resulting in (amongst others) Jimi Hendrix joining in late 1964 and quitting / being fired (depending on who you ask) some 6 months later in 1965. The backing band was known around this time as "Little Richard and the Royal Company", stage props including circa 5 or so extras dressed as Grenadier Guards standing on either side of the stage during concerts, probably a nod to the Beatles and England in general where they still had a monarchy which of course would be fitting for the king of rock, Little Richard.
Apart from playing live with little richard Jimi took part in at least one studio session. Richard had signed a contract with Vee-Jay in 1964 and recorded several new versions of his old hits as well as new material for the label during 1964-65. Vee-Jay closed down in 1965 and the recordings made for the label have since been endlessly re-issued. Vee-Jay didn't keep proper logs of the sessions or part of the information has since gone missing, in any case much is left to guesswork.