+1 for Red Storm Rising.
It's one of his first books, co written with another author, Larry Bond. Outside the Jack Ryan universe, but still his best book, even though it's a collaboration, IMO. One of the best cold war/WW3 fiction novels out there, still.
If you want to stay in RyanVerse, I would say Without Remorse is the next best book to read, set mostly in the time of the Vietnam War, fantastic book.
Or, you could always start at the beginning - read Red Storm, then since you've read Hunt for Red October, read Patriot Games next, then just go down the line of the Jack Ryan series, skipping or re-reading Rainbow 6.
I prefer his earlier works, from Hunt to around Bear/Dragon, after that, not so much. I remember as a kid, touring about the world with my Pipe Band, in every airport or plane cabin during the 80s and early 90s, it seemed as though every 2nd person was reading a Tom Clancy paperback. The year Patriot Games came out, I swear there was nothing but that blue colored book on board a long flight or two that summer.
I think after his divorce he became disinterested with writing, and had a lot of ghost written series, and even his "main" line of books were often co-written with little participation from Clancy, and it showed in the writting. Post 2000 or so after the Bear and the Dragon = sharp decline in quality, at least IMO.