There isn’t really a need for yeoman, at the time of TNG.
Well, that depends on the
definition of the role of Yeoman. Even the USN
can use them in wider roles than they usually do (because they also have other ratings for that):
The duties performed by YNs include preparing, typing and routing correspondence and reports, and organizing and maintaining files. They receive office visits and handle telephone communications.
YNs operate personal computers, word processors, duplication, audio-recording and other office machines. They perform office personnel administration, maintain records and official publications, and perform administrative functions for legal proceedings.
Yeoman serve as office managers and perform other various clerical and administrative duties.
Therotically, YNs can perform any equivalent duties to the Aviation Maintainence Administrationman (AZ) or the broadly equivalent RN rating of Writer Logistician (one of only three "admin" roles in the RN, the other two being Supply Chain Logistician [mostly Army Quartermaster/Navy Logistics Specialist/CG Storekeeper] and Catering Services Logistician [Culinary Specialist], with various "ship's serviceman" jobs sharing between the last two):
The smooth running of a ship is about much more than on-point kit. Our people’s welfare needs to run smoothly, too. As an HR Administrator (Writer), you’re in charge of Human Resources (HR), handling legal matters, financial admin, and looking after the welfare of your crewmates. Whether you’re advising your Captain about promotions or organising your crewmates’ pay, it’s up to you to make things happen. It’s a unique job in a unique environment, and a great opportunity to discover what makes us tick – and how we keep ticking, all over the world.
Much like how a comms officer isn’t needed anymore.
A
dedicated comms officer is rarely assigned to
the bridge (Kim is more of a Navigator/Engineer hybrid that covers COMMS as a collateral function, and IMO that makes more sense than
external comms and
primary internal comms being the responsibility of the Tactical Officer). However, we know from
Aquiel (TNG) that dedicated communications officers do exist and Ensigns and above could be assigned a variety of staff including -- Cryptological Tech (CT), Electronics Technician (ET), Intelligence Specialist (IS, shared with SECO/SecChf), Information Systems Tech (IT) or Mass Comms Specialist (MC) -- and that's for non-Bridge Officers*
Roles either evolve or die out, depending on what the needs of the times are. I do not see why anyone who is the captain of a Galaxy-class starship would need one. Seems to me that there would be an administrative assistant role in place of a yeoman, and those administrative assistants have their own office that they work out off, rather than reporting to the captain on the bridge.
The Captain of a Galaxy-class starship could be managing anything from 800 crew (2-3x that of the Connie) long-term to 15,000 crew and passengers for at least short periods, I have no issue with them needing
administrative support for such a role, although changing the title from yeoman (which in-universe was also something of the "captain's servant" in
TOS, reflecting norms up to at least the mid-20th Century) would be understandable IMO.
* This is why USS Discovery having
four "operations officers" on the bridge seems odd to me. Splitting off the spore-drive specific elements from Navigation (either part of Ops or CONN) makes some sense, but having a communications officer, a tactical officer and an operations officer on what was officially a
science vessel doesn't make sense to me. SDOps/DASH-Ops, Ops/Comms and Tactical would be more than sufficient IMO.