I think it's still very likely that Worf himself might eventually appear in a later season.
Your post got me thinking, were there any Klingons on the first series of DS9 (background or otherwise)? They definitely appeared on the second (Kaga, Kang, Kor and Koloth all make their first appearances), but I can't remember seeing any in the first.
For that matter, how about the third season of Enterprise?
If I'm wrong about either of those two, then the first Season of Picard could, potentially, be the first full season of Trek not to feature a Klingon. If anyone can think of examples of them in the above mentioned series.
TAS Season 2 is the first Trek season without a Klingon. But everyone and their mother ignores that show on this site. For shame.
Memory Alpha's a good tool, but here's a run through:
TOS Seasons 1-3 - Yes (Errand of Mercy, The Trouble with Tribbles, Day of the Dove)
TAS Season 1 - Yes (More Tribbles, More Troubles)
TNG Seasons 1-7 - Yes (Worf, but also Heart of Glory, A Matter of Honor, Sins of the Father, Redemption I & II, Rightful Heir, Firstborn)
DS9 Seasons 1-7 - Yes (Past Prologue, Blood Oath, The House of Quark, The Way of the Warrior, Trials and Tribble-ations, You Are Cordially Invited, Once More Unto the Breach)
Voyager Seasons 1-7 - Yes (B'Elanna, but 3-7 feature non-Torres Klingons in Flashback, The Killing Game, Infinite Regress, Barge of the Dead, Prophecy)
Enterprise Seasons 1-2, & 4 - Yes (Broken Bow, Judgment, Divergence)
Discovery Seasons 1-2 - Yes (The Vulcan Hello, Point of Light)
Short Treks Season 1 - Yes (The Escape Artist)
TAS Season 2 -
No
Enterprise Season 3 -
No
Short Treks Season 2 -
No
Picard Season 1 -
No, thus far
Also, Klingons appeared in every movie (Thanks Worf) except Wrath of Khan, Trek '09 and Beyond. They were cut from '09 and Beyond, but ships were seen in Wrath of Khan and '09.
The only series that went six episodes without a Klingon is TOS, because they first appeared in Episode 26 (Errand of Mercy). Klingons were in the first released episode of TNG, Voyager, Enterprise & Discovery, the second episode of DS9, the fourth episode of Short Treks, and the fifth episode of TAS. They were the first people seen (even before humans) in Enterprise, Discovery, and The Motion Picture.