When you say, "an effective replacement for a 1080ti" do you mean AMD's current top of the line card? (as the 1080ti was top of the line in its time) Or a similar launch price? (which for the 1080ti was $699) Because that would be as @johnnyenglish suggests the RX 9070XT.
Or do you mean equivalent performance in modern AMD hardware? Because you could get equal performance from as little as a 7600XT.
If you answer these questions we can better estimate what level of performance fits your need, system and budget.
What resolution and FPS do you want to game at?
What is your CPU/RAM/PSU?
What is your price limit?
Ryzen R7 5700X | B550 Gaming X | 2x16GB G.Skill 3600 | Radeon RX 7900XT
Ryzen R7 5700G | B550 Gaming X | 2x8GB G.Skill 4000 | Radeon Vega 8 IGP
Ryzen R5 5600 | B550 Gaming Edge | 4x8GB G.Skill 3600 | Radeon RX 6800XT