一般情况下不用seek for,因为这不是词组.除非是这种情况：They are seeking compensation/damages [=they are trying to get money] for their loss.在这句中for their loss是一个短语,不是什么seek for.
Seek
1 :to search for (someone or something) :to try to find (someone or something) 找(人或物)
▪ He is seeking employment.[=he is looking for a job]
▪ The office is seeking a salesperson.
▪ The prince is seeking a wife.
▪ Snakes seek the sun to warm their bodies.
▪ thrill-seeking travelers [=travelers who want to have very exciting/thrilling experiences]
2 :to ask for (help,advice,etc.) 寻求
▪ You should visit your doctor and seek his advice.
▪ You should seek medical help immediately if you experience any chest pain or shortness of breath.
▪ The church is seeking donations/volunteers.
3 :to try to get or achieve (something) 争取
▪ He sought revenge for his son's murder.
▪ During the war,she sought asylum in Spain.
▪ They sought refuge in Canada.
▪ The company is seeking new ways to improve service.
▪ The mayor is seeking reelection.
▪ She seeks perfection in her work.
▪ attention-seeking behavior
▪ Immigrants come to America to seek their fortune.[=to try to become rich]