Character mistake: When James Greer reviews Jack Ryan's military record, there is an entry that states he received the Marines Corps 'God' Conduct Medal. The word is meant to be Good. (00:31:09)
Continuity mistake: When Matice is given the coordinates and writes them down, his handwriting changes a few shots later.
Answer: As he is the author who created the Jack Ryan character that was adapted into a successful movie franchise, he could be credited as an executive producer for any TV or movie projects both before and after he died. It was announced in 2015 that the series would be produced for Amazon. Clancy died in late 2013, and he probably was involved in the series' earliest stages or discussions just prior to his death, and therefore would be credited posthumously. The title of TV or movie "executive producer" is fairly broad and can include one or more function, including securing financing, production oversight, creative input, script consultation, story concept, and more. Clancy's estate would likely continue to be involved under his name following his passing and receive profits and royalties.
While his estate would receive the profits, it's not automatic that Clancy would receive credit as a executive producer just because he wrote the novels. Authors like Michael Crichton, Douglas Adams haven't been credited as an executive producer after their death for use of their characters and works. Clancy's estate must be involved in the production in some way and rather than credit the estate, they credit the man.
Most likely his estate would be involved, through surviving family members, lawyers, etc. to act on his behalf in his name. No one said it was "automatic." It would have been a contract arrangement made while he was alive and that would continue posthumously. Whatever Michael Crichton or Douglas Adams did was a different arrangement for whatever reason they chose.
Nothing in your answer suggested anything about a contract arrangement (which if true would be the reason). You implied it was automatic. You said "as the author...he would be credited...for any...projects", but that simply is not true.