A Welsh lady's cat (7)
I believe the answer is:
persian
'cat' is the definition.
(I've seen this before)
'a welsh lady's' is the wordplay.
'a' becomes 'per'.
'welsh lady' becomes 'sian' (common Welsh name).
'per'+'sian'='PERSIAN'
(Other definitions for persian that I've seen before include "Type of cat or carpet" , "Iranian language" , "Long-haired cat" , "From Iran?" , "Breed of cat" .)