Promotion possibilities are the same as any law firm - the opportunities are there and if you want them you have to work toward them.
Graduates become qualified solicitors in their first rotation. The firm sponsors PLT which is generous, although market-standard for larger commercial firms. There are x3 6-month rotations and settlement occurs after 18 months. Regarding later career progression, while all lawyers have a nice scope for progression based on their appetite for hard work and performance towards partnership, I believe DLA has shown that strong performers can be promoted based on merits regardless of PQE. This may be considered 'early' (relative to the norm).
Depends on the team and the Partner you are working for, however juniors take a lot longer to climb up the ranks