Dog having to sit up with a cup (6)
I believe the answer is:
curtis
'up with a cup' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.
'dog having to sit' is the wordplay.
I cannot quite understand how this works, but
'dog' could be 'cur' (both can mean a despicable person) and 'cur' is found within the answer.
an anagram of 'sit' is 'tis' which is located in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Another definition for curtis that I've seen is " Hollywood actor".)