Were there cold war era submarine clashes that were suppressed to public knowledge?

Probably.

Yes. This is one of the hits I got when I googled. ‘declassified military information about submarines during the Cold War’

https://www.cnet.com/news/cold-war-collision-us-and-soviet-subs-crashed-cia-memo-reveals/

Not sure, but I always had my suspicions about the disappearance of the U.S. Nuclear sub Thresher. I think that’s the one that came up missing near the Azores. Another disappearance happened about the same time frame (late ‘60s) but the name of that one escapes me. I always figured they were sunk by Soviet subs.