A tee time was a designated time when one's game of golf was to begin.
In 2377, taking up golf as a new hobby, The Doctor booked a tee time in the holodeck. after B'Elanna Torres gave him a guilt trip, he gave up his three hours of golf to her and Tom Paris so they could have the holodeck all to themselves for a romantic weekend. Later, upon learning that Paris would be flying the Delta Flyer in the Antarian Trans-stellar Rally instead, The Doctor mused aloud that he might be able to get that tee time back after all. (VOY: "Drive")
In 2378, The Doctor played Paris' altered version of The Doctor's holonovel Photons Be Free. Upon being chastised by "The Doctor" for being 24 seconds late, the "assistant", played by The Doctor, complained, "This is outrageous." "The Doctor" replied "What's outrageous is that I'm going to miss my tee time."(VOY: "Author, Author")