I would argue, “No, you don’t” and I’ll tell you why.
Continuous Improvement is a unified and team-driven process rather than a department.
It’s a complete culture shift.
There shouldn’t be a separate Continuous Improvement Department that’s driving change.
BUT
You do need a Continuous Improvement Leader.
This can be the business owner, someone on the team, or someone from outside the organization in a fractional capacity.
You definitely need someone to drive the boat.
If there is not any management of the continuous improvement efforts, they will not sustain.
The idea of continuous improvement must be owned by everyone, and all have roles and responsibilities in the efforts, with someone at the helm leading the change and keeping people accountable.
If you have some continuous improvement ideas but need help bringing them to life then reach out.