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Doubtful - they're upgrading the Akulas and Oscars, and building more Yasens and Borei. Plus the whole Delta IV fleet is still in service, with a few boats overhauled in recent years.
Only a couple of the Akulas and Oscars are getting major upgrades. The others only had minor maintenance done to them which means they will remain obsolete in weapons and systems so by the end of the decade are likely to be decommissioned. The Borei program is the most advanced in terms of construction thanks to them reusing those Akula hulls for the first three units. I do not expect the SSBNs to be an issue. But Russia is way behind in terms of attack subs.
The US has the opposite problem in that they have a mostly obsolete SSBN fleet and relatively modern attack submarines. But even then they are still operating some Los Angeles attack subs which is kind of ridiculous. Those hulls are really old by now.
Then again given the recent scandal about low quality steel being used in US submarines by forging the inspection certificates for submarines over the last couple of decades, perhaps they are better off retaining those relics after all.