If you're already qualified at level 3, you don't need to complete further training for insurance purposes.
As a comparison, I completed level 3 hairdressing where we did an entire unit on bridal hair taught by the college tutors, who were very good. However, if I decided to specialise in bridal hair, I would definitely consider attending additional courses covering special occasion/bridal hair run by well known trainers to enhance my existing knowledge and to include in my portfolio as a marketing opportunity.
If you were the client and researching potential MUA's for your perfect day, would you opt for the 'beauty therapist' or the 'fully qualified bridal specialist MUA who completed additional training at X school of make-up'.