Could Italian fast battleships have saved HMS Tiger?

Would new Italian fast battleships have led the Royal Navy to retain HMS Tiger instead of Iron Duke?

Probably not on their own; the Royal Navy could reinforce the Mediterranean, and Tiger only becomes useful through an expensive, extensive reconstruction.

Three Italian fast battleships would alter Mediterranean deployments more readily than they would justify keeping Tiger. Iron Duke remained the better training ship, while an unmodernized Tiger was too vulnerable for 1940s combat. A major reconstruction could make Tiger useful alongside Renown, but would require new machinery, armor work, modern guns, dual-purpose weapons, and extensive anti-aircraft additions.