1026. When Snape died, the first person there to greet him was Lily. She walked up to him and punched him in the face, demanding answers as to 'WHY THE HELL DID YOU VERBALLY ABUSE MY SON FOR SEVEN YEARS???'
Headcanon that sometime after he loses Clara, the Doctor goes on a rock band tour, and as an encore he always plays a guitar solo that he calls “Clara” (because what better way to attract a young(ish? He can never tell, but the clothes scattered around a room he doesn’t remember look vaguely youthful) woman than with a rock concert?). This encore becomes, improbably, wildly successful, and everyone’s humming it for weeks till it inevitably fades from their memories and they move on to the next song.
Clara is in her late teens at the time, and the song catches her fancy when she’s setting her new ringtone. It’s named after her, she says, only half joking (even then she is certain she is special, set apart for something amazing), and chooses it. Never caught the band’s name, but then she’s never been interested in that sort of thing, she thinks, humming the tune absently.
When the Doctor starts strumming chords in the Tardis, after Skaro, she is startled. He will stare at her, gentle in his intensity, and plink out a chord, then another. (He won’t tell her what he’s doing, and she doesn’t want to push in case he decides to stop playing altogether.) Something about the music always reminds her of late-night conversations with far-off friends in college, and the day she found out she’d been offered the job at Coal Hill, and the moment of breathless dread when she’d called Danny, ready to tell him everything (but that comes far too close to remembering the moment when the phone went dreadfully silent, and her mind skates away). She’s not sure why it sounds so familiar. It’s probably just another of the Doctor’s many anachronisms.
It’s not until she meets the Doctor in a Utah diner that she realizes what the song had been.