The meaning and the grammar of the sentence “Natur trägt Begeisterung” is correct??
The grammar is correct. Reducing the phrase to three words (no articles etc) makes it look like a proverb. The problem is that there is no German proverb “Natur trägt Begeisterung”. Is the phrase a translation?
If the meaning is that nature enchants people I would suggest replacing “trägt” by “bringt”. “Trägt” is understandable, too, but unusual in this context. Furthermore, you would put an article in front of “Natur”, so an authentic phrase would be “Die Natur begeistert mich/die Leute” or “Die Natur bringt (mir/vielen…) Begeisterung”.