Yes, and in fact this is explicitly the business model[0] of ISO MPEG and ITU VCEG. They pay for their basic research by letting participants patent and license the resulting standards-essential inventions[1].
HEVC/H.265 has been in development since 2004, i.e. right after AVC/H.264 was published, and took almost a decade to actually be standardized. There's even an H.266, which started in 2017, a few years after H.265 was released. Though the primary concern of patent holders is not AVC patents expiring. Those patents actually aren't that valuable, because AVC is licensed way too cheap. MPEG-LA had negotiated a very generous free rate for online video[2], in response to MPEG-4 ASP (aka "DivX :-)") basically not getting much use online.
What patent owners want is to go back to the days of MPEG-2 where they were making money hand over fist just for owning a functional codec. They even sacked Leonardo Chiariglione, the founder and head of ISO MPEG, because he was trying to change ISO's patent policy to be more favorable to developing royalty-free codecs.
[2] Which is why YouTube's allowed to use H.264 without paying $$$ for it. Before that, they used whatever codec was available in Flash Player. Adobe (and Macromedia before it) used On2 VP6 primarily because it had no patent licensing royalty; before that they'd used H.263.
Somehow I suspect HEVC suddenly became a thing in the past few years precisely because AVC patents are expiring.