In general, schools are looking for recommenders who know the candidate very well, on the basis of an experience that is as long as possible and as intense as possible.
You can provide LOR from previous supervisor, as long as he can write it with high level of excitement and attest to your leadership and management background.
Make sure your recommender can answer the following questions asked by Cambridge:
1. Elaborate and / or provide us with concrete examples if you have rated the applicant as below average, outstanding or exceptional on any of the qualities in the 'Rate the Applicant' Section.
2. Describe what you like most and least about working with the applicant.
3. Tell us about any particular weakness the candidate has compared to other peers / team members that you regularly work with.
4. Describe the applicant’s attitude and behaviour when working with: (a) managers/supervisors (b) peers (c) subordinates.
5. Suggest what you think the applicant will be doing in ten years.