The most obvious answer would probably already be on the team and that is Harrison Ingram, he was signed to an exhibit 10 deal but they could just upgrade his contract to a standard deal and have him on the regular roster. Ingram hasn't shown much in his 2 years with the Spurs appearing in just 12 games. He has played well in the G-league though over 2 years averaging 14/10/4/1/0 on 45/31/60 splits. This wouldn't be a fancy choice but could be the easier one from the Jazz's perspective.
The Jazz could also choose to just upgrade one of their 3 players currently on a 2-way deal: Blake Hinson, Tamar Bates and Trey Alexander. Hinson would probably be the best choice as having an obvious NBA skill with his 3 point shooting and having a track record playing NBA minutes with the Jazz while they were tanking last year.
On that note the Jazz could look to sign one of the players they had on 10 day contracts during the late season tank last year to give them a bigger chance. Bez Mbeng, Hayden Gray, Andersson Garcia and Kennedy Chandler. All who played minutes with the Jazz last year, Bez Mbeng would probably be the most interesting choice for me as he is someone with extra ball handling and passing chops that could help the Jazz as well as a good perimeter defender. Chandler perhaps had the best run with the Jazz but just might be to small to get another guaranteed contract.
The most popular answer to this question would likely be fan favorite last year Kevin Love, Love wasn't expected to stay in Utah after being traded but he decided to stay and was a great locker room presence as well as being solid in the minutes he was given. Averaging 6/6/2/0/0 on 39/37/34 in 37 games. I think there could be multiple other teams interested in adding Love as a veteran, I think all 3 of his other former teams would also be interested the Timberwolves, Cavaliers and Heat could all use some additional depth and leadership. He could also reunite with Lebron in Philadelphia or sign with the Lakers but the Jazz would definitely welcome him back.
What do the Jazz need most with the 15th spot? I would argue a guard would be the most helpful this far down into your rotation or just go with someone like Love that is purely their for leadership. The Center is what the team needs the most but their isn't someone game changing to sign here really or else the Jazz would have already tried.
Option 1: Gabe Vincent, Vincent has been to put it lightly pretty terrible ever since he left the Heat in 2023. He could offer the Jazz some ballhandling and passing in a much reduced role, and hope his shooting could come back to him after the Monstars seemingly stole his ability to shoot. Last year in 53 games with both the Lakers and Hawks he averaged 4/1/1/0/0 on 35/34/87 splits which is pretty damn bad, but he is only 29 and maybe the Jazz think that he can help alleviate some ball handling pressures and give some guidance to some young players.
Option 2: Aaron Holiday, Holiday has much better counting stats last year in 57 games with the Rockets he averaged 5/1/1/0/0 on 41/39/85. Holiday brings a scrappy energy that could help this Utah bench he is honestly pretty similar to another Rockets player last year that the Jazz signed in Josh Okogie.
Option 3: Bruce Brown, Brown is probably the best player I've mentioned thus far and is probably an unrealistic option as I'm sure Brown is waiting to sign with a team destined to compete for a championship, the Jazz are set to make a leap this next year but not for a championship quite yet.
Option 4: Gabriele Procida? The Jazz have the rights to the former 36th overall pick, the 24 year old Italian currently is on a multi year deal with Real Madrid but has a NBA clause allowing an oportunity to sign with an NBA team if he so wishes. Procida averaged 5 points on 52/41/78 shooting last year. He hasn't quite developed as many hoped when he was drafted but the Jazz could still have some interest in giving the forward a NBA roster spot.
2 former NBA Players campaigning to get back in the league. Victor Oladipo and Spencer Dinwiddie have both been seen attempting to try and make their way back in the league could the Jazz be the team that gives them that chance? There hopes can go up after Ben Simmons managed to get a new contract with the Kings.