what is another way to say " highly sought out"? I am looking for an alternative phrase for this current phrase.
Something prized is often subjective but I think most here could use quaesitum for "highly sought out" but a general term is your 'objective desire'
Simply say "highly sought," the past tense of "to seek." The addition of "out" is superfluous, as "sought" conveys the desire for something not already possessed. Use "out" when using the present tense, as in, "We should seek out the best person for this position." Alternatively you might say, "This position is highly sought after..." but not "...highly sought out..."
With other adjectives directly related to seeking:
Exquisite: sought out, fine and dear
Recherché: rare, choice, sought out
You could also rework the sentence using a noun which suggests the desirable qualities sought:
Paragon: a model of excellence or perfection "We are looking for a paragon of good taste."
Apotheosis: the perfect example "We seek the apotheosis of the resolute factotum."
Consider "highly sought after" and "highly prized."