hold sb's feet to the fire

hold sb's feet to the fire AND keep sb's feet to the fire (to pressure someone to consent to or undertake something) — беспощадно, безжалостно давить на кого-л. (с целью добиться чего-л.); надавить, нажать

Example 1: Put his feet to the fire! — Нажмите-ка на него как следует!

Example 2: The only way you'll get him to agree is to hold his feet to the fire. (thefreedictionary.com)

Example 3: Call him up, and hold his feet to the fire. I want you to call him every day until the product arrives, and if you have to, tell him that we may have to look elsewhere if he can’t deliver. (openenglish.com)

Example 4: It was time to hold the old boy's feet to the fire, find out what he really knew about the company.

Related vocabulary:

[hold a gun to sb's head]
[twist sb's arm]

This idiom alludes to an ancient test of courage or form of torture in which a person's feet were so placed (пытка прижиганием пяток)