most likely AK 192 single 130mm gun same as in Gorshkov. But we will see.
Why put the gun of a frigate on a cruiser?
Kirov is a 25,000 ton project and yet it only carries 174 missiles whereas US destroyers carry 122 missiles for 9,000 ton displacement. Why is that?
The Kirov was the first ship to use vertically launched missiles, but the design of the vertical launch systems was different from western navies... they used rotary launchers that might have one hatch for 12 missiles on a rotary launcher system. The space underneath the launcher is huge and the missiles are not packed very efficiently because each missile in the rotary launcher had to be able to be accessed directly under deck.
Replacing those rotary deck launchers (used for S-300F Rif and Rif-M missiles and also the TOR missiles) would dramatically increase the number of missiles that can be carried.
Also the Russian missiles are significantly larger than western missiles... the 20 Granit missiles for instance are huge 7.5 ton supersonic long range anti ship missiles that the west really has nothing comparable to at all. In the upgrade these 20 launch tubes are being replaced with 80 launch tubes for a variety of missiles including Onyx which is a 2.5 ton missile with longer range and higher flight speed.
The 96 Rif type missiles could be replaced directly by four times that number of land based 9M96 missiles, which would mean 384 x 150km and 60km range active radar homing shorter ranged air defence missiles.
The main problem is that they have been focusing on smaller ships and Redut missiles rather than bigger longer ranged missiles.
Before they started upgrading the Kirovs there was no need to developed missile launchers for missiles bigger than the bigger 9M96 because corvettes and frigates don't need to engage targets beyond 150km in range and wont be needed to defend other surface ships except as part of a unified air defence.
The real problem is that they have not spent a huge amount of money on the Kirov upgrades... presumably because they are intended as stopgaps and eventually the new cruisers they will build to replace them will need to carry new weapons that might not fit existing launchers... like a naval S-500 missile for example.