After Clancy passed, the continuity got handed off to other writers. Those books kind of do their own thing, sometimes resetting Ryan's age or status. I'd treat the 'Clancy Universe' books as a separate, looser series after 'The Teeth of the Tiger'.
Chronological order is the way to go if you hate timeline jumps. 'Patriot Games' (early 80s), 'Red Rabbit' (early 80s), 'The Hunt for Red October' (mid 80s), 'The Cardinal of the Kremlin' (late 80s), 'Clear and Present Danger' (late 80s), 'The Sum of All Fears' (early 90s), then the big shift to 'Debt of Honor' (mid 90s) and 'Executive Orders' (late 90s). The later books, like 'The Bear and the Dragon', jump to the 2000s. This order avoids those 'wait, when is this?' moments.
Don't overlook 'The Cardinal of the Kremlin'. It's not first chronologically, but it's a masterclass in Cold War espionage and runs parallel to some events in 'Red October'. Jack is deeply involved in the high-stakes spy game here. The reason I mention it as a potential start is that it establishes the Russo-American tension that defines so much of the series. You get a real sense of the global board on which Jack plays. Starting with a 'middle' book can work because Clancy always recaps enough. This one has less of the family drama and more of the pure intelligence puzzle, which is what some readers love most about Clancy.