It depends
Yeast extract is sometimes made from brewer's yeast left over from beer production, which carries barley protein. The National Celiac Association and Gluten Intolerance Group both advise avoiding it without a gluten-free claim. Marmite, a yeast extract product, has tested around 30 ppm.
Yeast cells broken open so the savoury compounds inside can be used as a flavouring. That is all the term specifies — it says what was done, not what it was done to. The yeast can be grown deliberately on molasses, or it can be yeast recovered from a brewery after fermenting beer, and both end up on a label as the same two words.
Because the two sources give genuinely different answers and the label does not distinguish them. Yeast extract from molasses-grown yeast is gluten-free. Yeast extract from spent brewer's yeast carries barley protein. The ingredient name is identical in both cases, which makes this one of the small number of entries where reading more carefully cannot help you.
A gluten-free claim on the package resolves it and nothing else does. Without one, yeast extract is worth treating as a no rather than a maybe, which is the advice both US celiac organisations give. It turns up most often in crisps and savoury snacks, stock cubes, gravy, soup, and anything sold as having a savoury or umami flavour.
CiCi reads this as conditional rather than safe, and clears it only on a gluten-free claim. Where there is no claim it says the label cannot resolve it and explains why, rather than taking the more common case and calling it the answer.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and the full nutrition panel. 360,000+ packaged foods are already read and waiting.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.