Yes — your sentence is grammatically correct.
- "This animal's" means the wool belongs to one animal. The apostrophe + s (’s) shows ownership.
- "wool" is the soft hair from the animal.
- "is turned into yarn" means people change the wool into yarn. This is called passive voice, and it is okay here.
- "for warm clothes" tells why the yarn is used — to make clothes that keep us warm.
Some simple alternative ways to say it:
- "The wool from this animal is made into yarn for warm clothes."
- "A sheep's wool is made into yarn to make warm clothes." (if you mean sheep)
- "The wool from these animals is turned into yarn for warm clothes." (if you mean more than one animal)
Great sentence — short, clear, and correct!