A sabbatical was a practice existing in several cultures, consisting of taking time off from one's career.
At some point before 2367, the parents of Willie and Jake Potts went on sabbatical, but arranged for their sons to remain on the USS Enterprise-D. (TNG: "Brothers")
William Riker, who during an 2367 undercover mission on Malcor III was taken to a hospital and discovered to have an alien physiology, lied to his doctors by explaining that his irregularities were the result of inherited genetic traits, which could have been explained by his doctor if she wasn't on a sabbatical. (TNG: "First Contact")
In 2369, after Jean-Luc Picard was turned into a child as the result of a transporter problem, Deanna Troi argued that some people would find it hard to accept a twelve-year old captain. After going over several alternatives to commanding a starship, Troi suggested that he take a sabbatical and focus on archaeology for a few years. (TNG: "Rascals")
In 2374, Ziyal took a sabbatical from a Bajoran university to visit her father on Deep Space 9. (DS9: "Sons and Daughters")