Client of copper oddly swears about cat (8)
I believe the answer is:
customer
'client' is the definition.
(I know that client can be written as customer)
'copper oddly swears about cat' is the wordplay.
'copper' becomes 'cu' (chemical symbol).
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
'about' is an insertion indicator.
'cat' becomes 'tom' (a tom is a male cat).
The alternating letters of 'swears' are 'ser'.
'ser' going around 'tom' is 'stomer'.
'cu'+'stomer'='CUSTOMER'
'of' acts as a link.
(Other definitions for customer that I've seen before include "Client (who's always right?)" , "Buyer of goods or services" , "The person who pays" , "Person buying" , "The person who is said in business to be always right" .)