This is an idea that popped into my head a while ago and was then pushed to one side and forgotten about. It's not a fully thought out idea, but I thought it might be interesting.
Set in the early-2380s, the Enterprise
-E was on a routine mission in a relatively quiet region of space (one unaffected by the war or any other major incident in the last few years), I'd imagine possibly a cameo from Sir Patrick if he was up for it as well as several new characters brought in for the pre-credits set up. All contact is lost with the ship and a full scale search is organised. One of the SAR ships discovers the E-E five days after all contact was lost, however it has minimal/no power emissions and isn't responding to hails. Scans show no life onboard and a search of the ship confirms it. The crew have vanished.
The ship is towed into dock and examined, but the logs have all been wiped and the computer core has been restored to its "factory settings", so there is no data available to shine a light on what happened. The team investigating the ship are at a loss, unable to pick up any radiation, transporter signatures, weapons blasts, nothing at all that would indicate what happened to the crew.
With no answers available and unwilling to let such a ship as the E-E languish in mothballs, Starfleet assigns a new crew to the ship and gives them a new mission: to lead a task force into the region and investigate it thoroughly.
Other than the Captain being female (preferably alien) I've no strong thoughts or opinions on the crew roster or composition, though I would imagine around nine; with a maximum of four humans (including human/alien hybrids) and at least four characters being women (all in uniform, no skimpy/clingy catsuits here).
The tone would be darker than TNG, given the era and setting, with an undercurrent of mystery (though only a few episodes would deal with what actually happened to the previous crew). The characters would have some flaws and issues to work through, making them a little more realistic and not so squeaky clean as TNG. There wouldn't be a space battle every episode, the focus being more exploration and character dynamics rather than alien-of-the-week. It would also have a more serialised approach (with a few stand alone episodes), but events that happened previously would have impact of future episodes--no VOY reset button.