yearn for (someone or something)

To have an intense, deep-seated longing or desire for someone or something, especially in a slightly melancholy capacity. I grew up in a tiny town in Kansas, yearning for the day I'd get a chance to move somewhere exciting like New York or L.A. All the girls in my class yearned for him, thinking he was this mysterious, brooding hunk, but he was actually kind of an awkward dork when you got to know him.

yearn over (someone or something)

To have a strong, tender, deep-seated sympathy for someone or something. I don't know why you insist on going to the animal shelters to yearn over the stray dogs and cats when you know we're not going to take one home with us. The whole world yearned over the country following the horrible attacks.

yearning desire

A deep longing. I want to see as much as I can on my trip to England because I've always had a yearning desire to go there.