seek sb/sth out

PHRASAL VERB
If you seek out someone or something or seek them out, you keep looking for them until you find them.
[V P n (not pron)] Now is the time for local companies to seek out business opportunities in Europe...
[V n P] Ellen spent the day in the hills and sought me out when she returned.

Merriam-Webster's Advanced Learner's Dictionary

seek

seek /ˈsiːk/ verb seeks; sought /ˈsɑːt/; seek·ing [+ obj] somewhat formal
1 : to search for (someone or something) : to try to find (someone or something)
• 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.)
• 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 a : to try to get or achieve (something)
• 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]
• They are seeking compensation/damages [=they are trying to get money] for their loss.
b : to make an attempt to do something
• Doctors have been seeking [=trying] to find a cure.
• The builders sought to make the bridge stronger.
seek out [phrasal verb] seek (someone or something) out or seek out (someone or something) : to search for and find (someone or something)
• His parents sought out the best doctors in the field.
• White blood cells seek out and destroy infections.