Carr-Smith joined the Bath academy when he was 13 and made his league debut in October 2022, while he has also played for England Under-20s.
Along with Neil le Roux, Carr-Smith is one of two scrum-halves at Bath behind first choice Ben Spencer.
“I think ultimately my goal is to become the number one scrum-half here, I know you’ve got to become the number two first. I’m trying to do that and put some good performances together,” Carr-Smith said.
He called England international Spencer a “big inspiration”.
“It’s pretty cool to train and test myself against him every day. He’s been doing well with England at the moment so I see that as an extra motivator to try and push him as much as possible. It is exciting.”
Carr-Smith said he had spoken to Bath’s head of rugby Johann van Graan about what areas he needs to work on.
“The conversations with me have just been around working on my running game, I feel like that’s a big strength of mine and one I can continue to work on,” he said.
“Then when I get my moments how can I show that in games.”
Bath play Bedford away on Saturday in their final cup group game and as the only team unbeaten in their pool will be favourites to win the group and seal a place in the quarter-finals.
