Information for new junior officer

I’m not sure what’s in mind to introduce Lt. Gabriel Grant to the crew. I suppose the easiest way is that he is a new addition to the crew being picked up at a station or planet like Riker was in Encounter at Farpoint.

That way he and I could meet all the characters fresh . But is there any info such as the name and class of the starship and the captain’s reputation that he may know?

Sorry, I did miss your questions.

The crew roster is here.
The ship is the USS Independence, a Sovereign class starship.
The mission is a five-years mission, to explore the galactic fringe and perform deep scans of the globular clusters neighbouring our galaxy (it means you're on your own).

Lt Grant may very well be one of the 863 862 crew members of the Independence. He may just come under the spotlight because of his skills (he's a tactical officer + some diplomat training).
There is no real possibility, storywise and currently, to introduce him from the outside. The ship is already too far into unknown regions.

If you look at the roster, you'll see the tactical department head has no listed team members. Lt Grant may just be one of them (so I add him to the roster in this section).

On events that happened on the Independence, we're just at the journey start so...

• The USS Independence was entangled in resolving a worker strike on an agricultural world, that was threatening the food supply of a colony. It ended with the workers forming a semi-autonomous enclave on the planet, some sabres rattling and a new specie, the Dracartans, who invited the USS Independence to a formal meeting
  
• On the way to the meeting with the Dracartans, the crew decided to investigate the planet Hrotha, whose atmosphere was leaking and was irradiated, following the potential disappearance of a retired Starfleet captain who passed by that planet. The away team, on a shuttle, crashed on the planet following unclear circumstances. Fearing for the crew, the captain managed to overcome technical difficulties and have the marooned Lt Cmdr O'Rourke and Lt Codanadal be beamed up. The crashed shuttle was later transformed into a wreck by orbital strike with the phaser banks. And the ship left the planet orbit.
  
• Still on the way to meet the Dracartans, a power conduit explodes on the Independence, cutting power of the long range sensors, killing one crewmember and injuring three. Investigation ongoing.
  
• Lt Cmdr O'Rourke refusal to attend the convocations from Cmdr Seyler leads to a clash in the sickbay between the Chief Engineer (O'Rourke) and the Chief Medical Officer (Seyler). Which is followed by another clash between Cmdr Seyler and Lt (Zhen) Idisha. The dispute is carried over to the captain.