When you return to the ship from the salarian’s homeworld, several important things will happen. First, you will discuss the possibility of developing and mass-producing a cure for the genophage with Mordin. The scientist will say that he will need a tissue sample from both of the krogans onboard, and while the krogan diplomat will try to assert his dominance over the female specimen, she will deny him and move to the lab downstairs. Victus and the krogan diplomat will also each ask to speak with you in private. These conversations will each lead into fairly involved side quests. You will have to do at least one to continue with the story, although you do not have to do both.
You will have several opportunities to earn Paragon or Renegade points during the conversations, but nothing major. After the cutscenes have ended, speak with Victus and the krogan diplomat to learn of a secret turian mission on the surface of the krogan’s homeworld, Tuchanka, and the strange disappearance of a krogan squad on the outskirts of the galaxy. Although you only have to do one of these missions, you should accept and complete both, as they are each quite significant in terms of content, experience and items gained, and story.
From here, head out and speak with all of your other squad-mates. If you didn’t speak with Liara and James on your last visit to the Normandy, you can do so now, as their dialogue will not have changed since the last time you were on the ship. Liara will, however, have some new information for you from her Shadow Broker contacts. Head down to the Shuttle Bay to find Lieutenant Cortez crying at his station. He will be listening to a recording. Speak with him to console him and learn of the genesis of the recording.
Find your other squad-mates and speak with them, too, to develop a rapport with them. Garrus is in his usual spot near the Weapons Bay. Don’t forget about EDI, either. She will be in the ship’s cockpit with Joker. If you haven’t spoken to Joker since EDI’s transformation, you can get some funny dialogue from him here too. Finally, check your email to find that Kaiden or Ashley has been proposed Spectre status and is waiting on another visit from you. Head to the Citadel before completing any further missions and speak with your wounded companion in the Huerta Memorial Hospital. Ignoring them can make them bitter and resentful towards you, while heading to the hospital will improve your relationship with them and mend any scars left over from the events of Mass Effect 2.