Unfortunately Little Mill didn't maintain them and they are not usable now.
Peter Bowen is in Pembrokeshire which might be nearer depending on which side of Carmarthenshire you are.
There used to be a good gallop at Bryn Llewellyn's yard at Felindre but i don't know if that has been maintained.
There was someone who had gallops in Porthrhydd, but I never found out who they belonged to!
May be worth contacting Debra Hamer?
I used to take my TB galloping at Pendine beach, and know some who point to pointed who used to work them at Llanlwni mountain, but it would be best to go with someone to the latter as the safe area for galloping is a bit hard to find.