From your list, I think Tinsley sticks out like a trendy sore thumb. Blair(e) is ok, but it's kind of 80s-ish to me. I think Elise and Clara are the prettiest and most timeless. Whether or not that matters to you is a different matter.
I think Elise is a little overdone as a mn, so it would be cool to hear it as a fn. However, Elise Clara is not a very rhythmic combo, and neither is Clara Elise.
Elise Blaire is the best combo of the three names, I think, but it sounds a little choppy. And Clara and Blaire can't be used together, either, because of the rhyming.
I vote Elise Blaire. I love Clara though, and Clara Annaliese would have a similar feel as using Elise.
Clara Elise is charming and my favorite, but it's a COMPLETELY different style from Tinsley Blair.
Blaire Elise is nice, not my style but a good combination.
Elise Blaire isn't bad, and I feel Elise is more "wearable"/flexible than Blaire, which seems like it has fewer stylistic options. Maybe think about sibling names and the direction you'd want to go with that.
Tinsley is so far outside my style I'm not sure what to say about it.