The Class 1 shuttle was an early design of Federation shuttlecraft.
Owen Paris used to take his son Tom up in an "old Class 1" during his son's youth. Tom later suggested using a Class 1 on the holodeck after Kes asked him to teach her how to pilot. (VOY: "Fury")
This may be an alternate name for the S class shuttle, which Tom stated that he first learned to fly in, or likewise the class of the family shuttle Paris sank in a lake at sixteen.