Yes, you can replay again for the rewards. In many missions replay even gives you a choice of additional new rewards as well.
STO is about my Liberated Borg Federation Captain with his Breen 1st Officer, Jem'Hadar Tactical Officer, Liberated Borg Engineering Officer, Android Ops Officer, Photonic Science Officer, Gorn Science Officer, and Reman Medical Officer jumping into their Jem'Hadar Carrier and flying off to do missions for the new Romulan Empire. But for some players allowing a T5 Connie to be used breaks the canon in the game.
Perfect! Thanks! So much of the game is different now that I didn't know how it worked.
I had a level 20 Klingon with a Breen officer... probably not happening anymore. LOL
I also got really confused when I started a new Fed character and couldn't advance my Klingon storyline mission. Finally I realized that the constant buzzing asking me to do the Spectres mission was actually in sequence instead of just a feature episode I could do when I wanted!