What I would want from a new Thief game:
Appropriate the Darks Souls (and Metroid Prime etc) free-roaming world design formula. I.e. make the entire game a single interconnected environment, with many diversely themed areas that densely link up to each other in interesting ways. This should not be a stretch for Thief because its already the gold standard for how we design individual mansion and city missions. (It doesn't need to be gigantic though. Think how awesome Iris was.)
A new city with new cultural inspirations. This is one reason I think Dishonored feels like a worthy spiritual successor despite dropping the ball somewhat on gameplay. An Arabian knights tinged Bagdad/Cairo like setting would be interesting to skulk in, or a city with shades of 19th century Hong Kong/Shanghai.
A new main character who is not a Garrett reboot. If anything our new MC should be a thematic foil to good old Garrett: someone in a similar situation but for different reasons, with a different outlook and character arc. Thief 2X did this well. For instance I would be fine with the MC being a young acolyte of a new Keeper order started by Garrett after Thief 3, but don't have him/her leave to become a thief out of hubristic pride. Have them turn thief out of desperation, post some disaster or failure. Make it something they are distressed over, then over time grow to appreciate the monomythic import of being "The Thief" in the Thief-verse.
New factions for a new story and MC. While Hammers, Pagans, Keepers, town guards, and crime lords, were cool and thematic for Garrett's story. Our MC should have their own friends and foes. Maybe the city ruling families are a bunch of ancient mage clans. Some are austere isolationists with ties to organized crime, others internationally minded reformers who are embracing the City's steam punk tech. Maybe instead of pagans the new city has a cults of ancestor worshiping necromancers. Maybe the new Keepers are a dysfunctional confederation of ego driven lunatics and schemers, suffering from the neglect of an absentee leader who only seems to care about balance.
It's still a detective story at heart. All the good Thief games are about slowly and sometimes incidentally figuring out who is the big bad and how your sneaky skills can stop them. That should not change.
Maybe incorporate some light immersive survival elements, perhaps in the mold of Pathologic, but probably less oppressive. E.g. have the MC need to steal so s/he actually has money to buy food and pay rent on someplace to sleep during the day. Otherwise hit them with penalties.
I would be fine with MC getting some supernatural movement tech like the Thief 4 Swoop or Dishonored Blink, but it should be late game only (unless the player sequence breaks, which would be a super cool option).