There are a decent number of old articles on Leggetts in that area. As you may have already found them in your research, I've just put a few notes referencing what the article is about, as it might help explain Edgar's various occupations:
Evening Star 28 November 1899
Inquest into death of Nathan Leggett death, which was from an accident in which he was thrown from his horse drawn "trap", and the coroner states that two out of three "accidents" requiring an inquest at that same location had fatalities to veterinary doctors. Edgar is mentioned as identifying the body, and his occupation is given as "dealer"
Middlesex County Times 07 February 1903
Death of a highly respected James Leggett, 3rd son of Cornelius, born 1815, both veterinary doctors, university trained, lived Hanwell Suffolk. Well known farriers and vets etc. (Could this be Nathan's father?)
Evening Star 19 June 1908
Edgar Samuel Leggett, horse-breaker, Ipswich, charged with cruelty to a horse at Trimley. The owners of the horse thought that he was "a real horse doctor" and called him to tend to their animal. Edgar said he had succeeded his father in his business nine years earlier. and had never had a problem. However he made a very serious error, and the RSPCA and a "real veterinarian" was called in, and the horse had to be put down.
This article also discusses how anyone can practice animal medicine, as long as they don't refer to themselves as veterinary surgeons. The common term used for the untrained ones was "horse doctors".
East Anglian Daily Times 30 October 1908
PUBLIC NOTICE
EDGAR SAMUEL LEGGETT, S. JOHN'S
IPSWICH
Beg to inform his Clients that he still car-
ries his Practice on as usual, thanking
them for past favours, hoping to continue the
same.
Framlingham Weekly News 30 August 1913
Edgar Samuel Leggett of Saxmundham, pig dealer, getting fined (again) for no licence on his sulky. He also breaks colts and tends sick cows.
Edited to add missing words and the PUBLIC NOTICE article.