A word for 'something more' or 'missing from life'

"Longing" refers to almost exactly what you're talking about. Having a longing is probably described by the adjective "wistful." To have a longing is to "yearn." Those are the only three I could think of. I hope this helped in any manner.

Perhaps unfulfilled is what youu are looking for?

un‧ful‧filled
1 an unfulfilled hope, desire, dream etc has not been achieved: His dream of competing in the Olympics remained unfulfilled.
2 someone who is unfulfilled feels they could be achieving more in their job, relationship etc.

It's probably a wish, imagination, or a dream. Or something wishful as wishful thinking.

Toska.

It's a Russian word I found in an online article covering 20 words not translatable into the English language.

This feeling is:

Your life sucks, no one even bothers you, or belittles you, but you are just dust in the wind, invisible. One day you meet someone really special, who grasps your self worth and understands you, no, sees you.

You know you have everything you have ever wanted, or could ever ask for. You know you should be happy, you want to be happy, but you can't.

You feel as if something is missing in a very big way. A hole in you that you can't place. What is it? Why can't I be happy? What thing am I missing?

That is toska.

You are missing the purpose that defines your soul. You haven't found the thing that you love most. You don't even know what you love most, because you don't know what it is you are missing.

Toska.