Ummm, Steart Barton is where I used to be. It's between Wellington and Taunton so may well be a bit far. The current yard and new yard will both be too far for you by miles.
Depends what livery your after, Leigh Equestrian Centre is under new management, but i think they are only taking on part & full, could be worth a ring though?
Hillview Stables, Crewkerne has DIY Livery which is about 9 miles from Yeovil 01460 72735 or Cockoo Hill Livery Yard, Yetminster 01935 873399 about 5 miles away.