Summary
At 36 years old as a free agent in 2024, Beverley likely will only be looking at one-year minimum offers, especially after settling for the minimum in 2023. He is no longer a starting-level guard (although he did start some key games for the Bulls and Bucks late in the last couple seasons). He can still provide decent backup play, but that may not last much longer given his age and some regression already.

Since Beverley is not much of a ball-handler or play-maker, his best role is next to a ball-handling wing who can carry the load on offense. That allows Beverley to spot up from three, particularly from the corners where he is especially effective.

While not known as a shooter due to his relatively low volume of attempts, he has generally shot well in the past. However, he shot a career-low 34% from three in '22-'23, and wasn't much better in '21-'22 or '23-'24 at 35%, so he's been a below-average outside shooter for three seasons now. He's not much of a threat from inside the arc either. If Beverley can no longer hit shots at an above-average rate, it's hard to picture him being a helpful offensive player going forward.

The feisty guard was at one point known as one of the better perimeter defenders in the league, but has declined in that area in recent years. He can still compete on that end, but his excessive fouling, which often leads to teams getting in the bonus sooner and free throws on non-shooting fouls, might negate most of the value that he provides on that end, especially considering he has lost a step as he has aged. He also will start the '24-'25 season suspended for four games for throwing a ball at fans when the Bucks were eliminated from the playoffs, and you wonder if teams will still believe that the pros outweigh the cons for Beverley.
 
Cap Considerations
Beverley will be an unrestricted free agent with a $2.1 million cap hold and Non-Bird Rights. This means that the highest starting salary the Bucks could offer him using the Non-Bird Exception is $4 million. This should be enough to retain Beverley, since he settled for the minimum last summer. 

Other teams will have multiple ways to sign Beverley as even teams without cap space could possibly use the Non-Taxpayer MLE, Room MLE, or possibly even the Taxpayer MLE or Bi-Annual Exception to sign him. It's also likely that Beverley only gets minimum offers, and he may not even get fully-guaranteed offers.