Holy activity, Batman! I get locked up busy for a weekend and am behind almost a month in posting! 
OK, so let's see if I can post my own suggestions in a value-added way.
Ops: On some ships, the captain requires command officers to eat together. I don't think that's the case on the Peregrine but when the captain does call for an "officer's dinner" then Ops would be in charge of prepping the food and I could see that meal not coming from a replicator.
Additionally, clothing, linens, blankets, etc is all replicated but it is my understanding that the replicators don't produce something from nothing. Much like today's 3D printers, they need a base material to work with and those stores are something that Ops personnel oversee. Each individual onboard has a replicator ration that they're alotted and Ops helps manage that.
If any department needs something, they submit the equivalent of a Purchase Order to Ops. Engineering may have a need to replicate something outside of the ship replicator specs... Ops requisitions it for them through the nearest starbase. Science needs a particular chemical... Ops requisitions it. I believe that some starships have industrial replicators on board, but these still use source material and are regulated.
Quartering concerns, station upgrade coordination, department coordination of personnel, working with security to accommodate away team equipment needs, take care of shore leave situations, etc. are all part of the parcel. There are a lot of responsibilities that fall to Operations.
Quarters for Ensigns: I liked the first concept best, Eol. Maize has been on board the longest and it doesn't make much sense for her to have shared quarters but a noob receives a solitary bunk.
How does one delete characters from Trek Tools?