"Sought" is the past tense and past participle of "seek", e.g.
1. I am seeking a solution => I sought a solution.
2. I have sought a solution for a long time.
"Sought-after" can also serve as an adjective, e.g.
2. That book is much sought-after.
which means "many people are seeking that book".
All the best,
Student or Learner