I'd say take a page from TNG, DS9 or VOY then, when the new officer reports to the CO, keep it brief then get them both right on task, assuming their stations/preparing for launch. Spending too much time on the scene, unless they have or develop an intense relationship (good or bad) with one another, could lead to excessive exposition dump and doing too much telling instead of showing:
- If the Captain is more standoffish and impersonal, they might just want to do a Picard/Riker, seated behind their desk, scrutinising the new arrival before ordering them to do something either out of the blue or very mundane, to see how they deal with unusual orders or complain about the banal nature of the task
- If the situation is a little tenser, then it could be a Sisko/Dax/Bashir moment, fobbing the new arrival off on someone else whilst they continue to work the problem, so the new arrival then has to deal with losing the chance to make the first impression they wanted and risk putting their foot in it
- Or if the Captain prefers a more personable approach with their crew, then it could be a Janeway/Kim moment, with the CO making a joke before letting them know exactly the type of leader they are, they could even offer a coffee and ask them to take a seat, only to be interrupted by a matter that requires their attention
You'll know your characters better, so unless they're the type to have long philosophical debates with people they don't know, then keep it brief and on point. Work out the exact plot or character points you want the scene to highlight and build their interaction around that.