Full-back extends his spell in BS7 by two years with the option for a further year.
Clarke, 24, joined the Gas on a one-year deal following his departure from Rotherham United and made his debut against Mansfield Town in August 2021.
The Dubliner said: "I am delighted to get this over the line. It was tough at times last year with injuries. I just couldn't seem to get going but I'm fully fit now and can't wait to get the new season started so I can show supporters what I'm all about.
"Those last couple of weeks of the season are amongst my top football moments and securing promotion with this set of lads was brilliant. I've experienced League One before, and won promotion with Rotherham, so I'm looking forward to a good season."
On the defender's signing, Rovers boss Joey Barton said: "Trevor had a tough year last year but showed enormous character to overcome those challenges and provided an impact towards the closing stages of the season. Now, with a full pre-season behind him, I think he’ll show his full potential."