"Looked for" is the past tense of "look for", meaning searched for someone or something. It describes a completed effort in the past to locate a person, place, or item.
looked-for
True love begins when nothing is looked for in return. Antoine de Saint Exupéry
I lost my father was I 10 years old, and I always looked for a father. I missed my father very much. Anthony Quinn
Fernanda, on the other hand, looked for it in vain along the paths of her everyday itinerary without knowing that the search for lost things is hindered by routine habits and that is why it is so difficult to find them. Gabriel García Márquez
If the mother had never been in the oven, she would not have looked for her daughter there. Latin Proverb
The butcher looked for his knife and it was in his mouth. Romanian Proverb
Long looked for comes at last. Dutch Proverb