In Carmarthenshire after that (4)
I believe the answer is:
then
'after that' is the definition.
(synonyms)
'in carmarthenshire' is the wordplay.
'in' indicates the answer is hidden within the clue.
'THEN' can be found hidden inside 'carmarthenshire'.
(Other definitions for then that I've seen before include "Subsequently - previously" , "Once upon a time" , "Consequently" , "At that time; next" , "Afterwards - as a result" .)