Of course it's less simple than finding a 120 wRC+ bat and plugging him into the DH slot, though. Many players with bats that good play other positions, or believe they do, and teams would offer them (or their teams) more to play those positions.
There are 75 hitters whose combined 2022-23 seasons cleared 120 wRC+ or above. To shorthand who among those might reasonably be considered a DH, let's look at the 37 of those had 0 (full-time DH) or negative defensive value (per Fangraphs). Five of them already play for us. Here they are, listed in descending order by hitting prowess (wRC+):
Ohtani, Trout, Altuve, Goldschmidt, Yandy Diaz, Soto, Acuña Jr., Alonso, Nathaniel Lowe, Arraez, Devers, Olson, Carpenter, Riley, Pederson, Bichette, Harper, Will Smith, Noda, Yoshida, Nimmo, Jiménez, Refsnyder, Arozarena, Guerrero Jr., Donovan, Willson Contreras, Jansen, J.D. Martinez, Turner, Henderson, Pasquantino, Hoskins, Casas, Santander, Slater, Harold Ramirez
That's an exclusive group. If you further narrow it to right-handed batters, which seems preferable given our lineup, there are 20 names (excluding Refsnyder, and including the switch-hitting Santander).
But how many of those guys are actually available? Very, very few. We can fantasize about Trout, Goldschmidt or Alonso, but in the remote chance we'd acquire them, it would constitute such a massive roster makeover so as to defeat the exercise of merely replacing Justin Turner.
There are exactly two names on that list I could see the Sox acquiring to replace Turner next year: Eloy Jiménez and Anthony Santander. Eloy has one guaranteed year and two team options on his contract at reasonable salaries, and though he's only 26, he probably is a permanent DH at this point. It's quite possible the White Sox trade him in their rebuild, but I wouldn't bank on it, and it'd likely be costly. Santander has come up among trade targets before, but the O's are contenders now and don't need to move him, and besides, DRS and OAA have him as at least a roughly average RF (though a negative LF).
Of course, we could just plug Yoshida in at DH. Personally I'd like to give him at least another year in left field — he may improve, and anyone else would be equally punished by the Monster in the eyes of the metrics. And of course, this exercise just looks at recent history. It's isn't a comprehensive list of players who will put up a 120 wRC+ in 2024.
It may be easier just to guarantee Turner another $15M or so.