“My job requires me to put in a lot of late hours.”

You often have to work until late in the evening. You're telling an acquaintance about this situation. You say:

My job requires me to put in a lot of late hours.

(a job) requires (someone) to (do something)

Use this phrase to describe things that you have to do for your job:

My job requires me to travel a lot.

Being an emergency room doctor requires me to be on call at all times.

My position requires me to be at work at 6:00 in the morning.

put in (work)

To "put in" late hours means to work late a lot. The phrase "put in work" means to work hard, so that you can eventually accomplish something great.

I like to put in overtime whenever I can to make a little extra cash.

To become fluent in English, you've got to put in hundreds of hours of study time.

work late hours

"Working late hours" means staying at work late in order to finish all the things that you have to do.

There's a small difference between "working late hours" and "working overtime". When you "work overtime", it often means that you get paid extra for that time. However, when you have to "put in late hours" at work, you're usually not paid any extra.