Phrase for insatiable with positive connotation

Question

Is there a word or phrase with a positive connotation for someone who is never content with their standings, quite curious and always pushing for new heights?

Answer 1

I'm not sure this is close enough in meaning to the word or phrase you're searching for, but perhaps indefatigable would serve?

Answer 2

Such a person can be described as being not content to rest on their laurels. This certainly has a positive thrust: the attitude of aiming ever higher.

not rest on your laurels [COMMON] If someone does not rest on their laurels, they continue working hard to make sure that they continue to be successful rather than relying on the success they have already had.

Derivation: In ancient Greece, the laurel or bay tree was associated with the god Apollo. The winning competitors in the Pythian games, which were held in honour of Apollo, were given crowns or wreaths of laurel.

• We will not rest on our laurels. There is still much to be done.
• He never rested on his laurels but continually evolved as an artist.

[Collins COBUILD Idioms Dictionary, 3rd ed]

The expanded version is also common; here are several examples from the many to be found on the internet:

• Not content to rest on their laurels, Club President Sara Burbine Potter '91 and her dedicated Board of Directors forged another spectacular year ....

[Dartmouth Alumni]

• At Freed, our consultants are not content to rest on their laurels. Instead, they pursue ongoing professional development activities to enhance and hone their ....

[Freed Associates]

• But now, not content to rest on her laurels, Rowling is back for more. Her novel for adults, "The Casual Vacancy," was published last year.

[The Christian Science Monitor]

Answer 3

Although not being content isn't express in the meaning of this phrase, it could be taken to be implicit therein.

Push the envelope

If someone pushes the envelope, they do something to a greater degree or in a more extreme way than it has ever been done before.

The cinema director pushed the envelope of acceptable family entertainment.

[Collins]

Answer 4

aspirational

a : having or showing a desire to achieve a high level of success or social status

Contrasted with aspiring which carries the connotation of a someone who lacks success but has set their sights on one specific goal.

Answer 5

Edit: Prompted by the comments, I will express my preference for the word insatiable itself. However, I do understand your reserve, because while looking it up I see that some dictionaries associate it with all sorts of negative connotations. It is even said to be the synonym of greedy. About it Etymoline says (I underline the Latin origin):

incapable of being satisfied or appeased; inordinately greedy," early 15c., insaciable, from Old French insaciable "ravenous" (15c., Modern French insatiable), or directly from Latin insatiabilis "not to be satisfied," from in- "not, opposite of" (from PIE root ne- "not") + satiabilis, from satiare "fill full, satisfy," from satis "enough" (from PIE root sa- "to satisfy").

So basically, it means to hunger to a high, extreme degree for something, and whatever one hungers for determines if the word takes a positive or negative connotation.

You could very well praise someone saying:

His insatiable thirst for knowledge gave him no rest, always urging him to crave for more.

Yet, if you still reject the use of insatiable, you may prefer

perfectionist

a person who refuses to accept any standard short of perfection. (OxfordLanguages)

​a person who likes to do things perfectly and is not satisfied with anything less (OxfordLearners)

Collins gives this nuance:

a person who demands perfection of himself, herself, or others

So it can take a negative connotation when the subject expects perfection from others. But if you give it the right context, where perfection is expected of oneself, not of the others, it means what you describe. Compare

The designer is a perfectionist and that shows in his eyewear designs. (positive connotation)

and

He was a perfectionist who didn't suffer fools gladly. (negative connotation)

Wikipedia has a whole article about the psychological aspect of perfectionists. Although it deals more with the degeneration of this quality, it also states that

Perfectionists strain compulsively and unceasingly toward unattainable goals, and measure their self-worth by productivity and accomplishment. Normal perfectionists are more inclined to pursue perfection without compromising their self-esteem. Healthy perfectionists score high in perfectionistic strivings and low in perfectionistic concerns.