Vjylku

The Korred (Volo's Guide to Monsters, p. 168) is a CR 7 Fey that can be summoned by the Conjure Fey spell.

The description of the Korred has this bit of text:

Korreds have hair all over their bodies, but the hair that grows from
their heads is magical. When cut, it transforms into whatever material
was used to cut it.

Can I cut the hair of a conjured Korred with a blade made of precious material (Gold/Platinum/Adamantine/Mithril/etc.) to harvest lots of the material?

This plan is unreliable at best, as it relies on your DM being amiable.

The korred monster entry in Volo's Guide to Monsters actually has a quote from Volo covering this scenario:

There's a legend about a merchant who tried to cut a korred's hair with golden shears. The korred fed him those shears, from his swallow to his sitter.

Now, as you quoted, when cut, a korred's hair reputedly transforms into whatever material was used to cut it. Bone? Iron? Gemstone? Rules-as-written, unless your DM decides otherwise, whatever material was used to cut it.

However, the korred is a challenge rating 7 creature, with high armor class, over 100 hit points, the ability to burrow to escape, tremorsense, and a variety of other abilities. Only a high level character can pull off this heist with impunity.

Your main problem, though, is that conjuring one to harvest it is very chancy, and relies heavily on DM ruling.

Conjuring korred for fun and profit

Firstly, while the korred can cast conjure elemental, it is itself not an elemental, but a fey. You would cast conjure fey, which, using a 7th level spell slot or higher, can conjure a 7th level fey, which may include a korred. A party of level 13 or higher should have little difficulty fighting one korred.

However, the spell does not specify that the player gets to choose which fey appears, and as per the Sage Advice Compendium, the DM is ultimately intended to choose which creature appears, not the player:

A spellcaster can certainly express a preference for what creatures shows up, but it’s up to the DM to determine if they do. The DM will often choose creatures that are appropriate for the campaign and will be fun to introduce in a scene.

Your second big problem is that the conjured creature disappears if reduced to 0 hit points or 1 hour passes—you can't capture and enslave it and harvest hair indefinitely. So even if your DM gives you the korred, you have at most one hour to bring your golden shears and chop as much hair as it has right now, and that's while it's conscious and resisting all attempts to cut its beloved hair:

Korreds take great pride in their hair, and equally great offense at anyone who attempts to cut it without permission.

And even then, you're assuming that korred body parts don't disappear with the rest of the creature when the conjuration finishes. There's no general rule or Sage Advice entry on this, meaning, again, it's up to your DM.

This entire endeavor thus relies on your DM:

1. Allowing you to choose which creature you summon


2. Allowing conjured body parts to remain behind when the conjuration ends


3. Working out a rule for trimming a creature's hair in combat
   

Is it profitable?

The korred is a Small creature, and only the hair on its head. That's not necessarily much hair.

The length of the korred's hair is entirely up to the DM. Artwork in older editions show its hair as relatively short, but in 5e they're depicted as heaving dreadlocks. A google search suggests that an adult human's dreadlocks might weigh as much as five pounds, so a small creature, being around half the size in all three dimensions, probably has less than two-thirds of a pound of hair to make into gold (5÷8 = 0.625).

I can't find a figure for the density of human hair, but it's likely to be similar to that of hempen rope, which has a relative density of 1.35 g/cm³, while gold's density is 19.30 g/cm³ at room temperature: about 14.3 times the weight.

Shaving a korred will therefore produce at most 8.94 pounds of gold, which at a value of 50 gp per pound (as per PHB p.157) is worth only 447 gp.

By comparison, the typical Individual Treasure for a random Challenge 11-16 encounter (DMG p.136) starts at around 490 gp. By the time you can summon korred with imunity, it's not remotely cost-effective.

Now, if you could capture and enslave a korred long-term, you could make a lot more money. Given time, a korred is canonically able to craft a rope from their hair, a somewhat time-consuming process. A 50 foot hempen rope weighs 10 pounds, which if that much hair were turned to gold would weigh 143 pounds, worth 7,150 gold pieces.