How to improve velocity without sacrificing quality?

I'm going to assume you're a software engineer, so I recommend this masterclass on writing better code faster. In a nutshell, productivity gains as a SWE largely come from leveraging focus blocks and front-loading code planning so you don't face thrash on your code reviews.

For the future, I recommend attaching your level/company to the question or adding more context like what kind of work you do that you feel can be made more efficient.

How to keep the team members motivated all the time?

In a vacuum, the stronger the social fabric of a team, the more motivated its members are. I recommend this discussion on encouraging more networking amongst the team.

Aside from that, motivation is also correlated to quality of execution. If projects are exciting, deadlines are reasonable, and thrash is minimal, the team is generally fairly motivated and happy.