Can I classify a healthy population into clusters found in an injured population?
The dataset (population) that you used to define the clusters was a different one from the one you are looking at now (healthy population). That means you can’t use your clusters to categorize healthy people just like that, but your research question is not what cluster each person belongs to.

If your question is to see whether people are consistent in their movement strategy then you can use the information from the clusters you have, or any other clusters you just made up. The cluster assignment is a proxy (a simplified representation) of each measurement, and you’re trying to see if they are consistent from the cluster numbers of each measurement.

This seems to me to lead to results that are difficult to interpret. What if healthy people are consistently very close to a border between two clusters? Consistent, but jittering between the clusters.

I would say you need to drop the idea of using a cluster as a proxy. Let’s say your measurement is how fast people can run a mile, time after time. To know if they’re consistent, you would just look at the standard deviation for each person.

I guess your problem is that you have many measurements in each example, and you’re trying to simplify by using a cluster number rather than the actual measurement. That’s dimensionality reduction, to a single dimension, which is extreme, and I wouldn’t use clustering for it. Is it really necessary to reduce the dimensions, or would it be possible to define a consistency metric on the original data? If it’s not and you need to reduce the dimensions, I would first turn to PCA and if that’s not enough, maybe an embedding from an auto-encoder.