The past tense of put one's nose to the grindstone is also put one's nose to the grindstone.
The third-person singular simple present indicative form of put one's nose to the grindstone is puts one's nose to the grindstone.
The present participle of put one's nose to the grindstone is putting one's nose to the grindstone.
The past participle of put one's nose to the grindstone is put one's nose to the grindstone.