The obvious character to include is Tauriel, since she has a big role in the next two films anyway, and the obvious place to include her is in the White Council meeting, since Galadriel has nothing but contempt for Saruman and thus has both the motivation and the ability to conduct telepathic conversations with others during the meeting.
The Hobbit: An Unexpected Journey
Scene: Galadriel is participating in a White Council meeting at Rivendell (with Elrond, Gandalf, Saruman), to discuss rising threats such as the Necromancer of Dol Guldur, the Fomor, etc.
SARUMAN: Radagast? Do not speak to me about Radagast the Brown. He is a foolish fellow.
GANDALF: Well, he’s odd, I grant you. He lives a solitary life.
SARUMAN: It’s not that. It’s his excessive consumption of mushrooms. They've addled his brain and yellowed...
Saruman's voice fades away as Galadriel focuses on Tauriel, who is off doing tai chi elsewhere on the grounds, and speaks to her in her mind.
GALADRIEL, telepathically: OMG Tauriel, I can't believe he's sharing this vile boring gossip. My blood pressure is hitting the roof and I'm seeing red. Please distract me quick before these stupid lies start to addle my own brain!!!
TAURIEL, telepathically: LOL Galadriel! I'm actually really focused on my practice right now, but I'll share my thoughts with you to help you reach a state of calm: Breathe in, reach down, bend your knees, gather the air up from the ground...
GALADRIEL, telepathically: Ah, calm breathing, yes.
Galadriel is now also practicing tai chi in her mind.
TAURIEL, telepathically: ... continue bringing it up and up to your chest; now breathe out, reach your arms up to the sky; breathe in, slowly lowering your arms out to the sides; breathe out, moving your arms in front of you.
GALADRIEL, telepathically: You're the best, T! I feel so much better. I need to get back into taking tai chi and origami classes again; they really help me stay calm and focused. That reminds me, gotta get back to the meeting - I need to make a little revelation about the thing brought back from Dol Guldur. I mean, it should be pretty obvious, but not everyone here is playing with a full deck if you know what I mean.
TAURIEL, telepathically: Yeah, you mean the Witch-King of Angmar's Morgul-blade? Good luck with that - and peace out!
Tauriel's voice fades away as Galadriel focuses on Gandalf, and speaks to him in his mind.
GALADRIEL, telepathically: You carry something. It came to you from Radagast. He found it in Dol Guldur.