A „piece of the rock“ is an old expression that I frankly don’t hear much anymore. It kind of means to have or own a part of something. It’s fading from use and I don’t think I’ve heard anyone use it for years, and then it was only part of an advertising campaign on TV in the US when I did hear it. I’d avoid using it entirely as it’s somewhat archiac and actually very rarely used.

I‘m glad Victoria agreed with me so I know I’m not missing something, but I don’t think this expression „a piece of the rock“ ever was a part of English. I’m 59, so I’ve got some years on many people here, but I think this expression, which I have heard before, comes, I believe, from an advertising slogan that was invented (probably by some advertising company in New York) for a bank called „Gibralter Savings and Loan“, which no longer exists. It was on TV a lot in either the 60s or 70s, or both, and the slogan was something like, „Invest with Gibralter and own a Piece of the Rock!“ The Rock was a play on words referring to the „Rock of Gibralter.“ So, then the company went out of business or merged with someone else, the name changed and the advertising slogan got dropped. I’d bet that’s the history of it and why I’ve heard it before. So, yes, drop this expression. I’m pretty certain it was an invented advertising slogan from the 60s in the US and was never even a part of the language. It’s amazing to see some people have repeated it modernly thinking it was a real English expression. „The rock of Gibralter“ is an English expression, not used often, but that’s different.