Descendant of dissolute cousin not upper-class (5)
I believe the answer is:
scion
'descendant' is the definition.
(scion is a kind of descendant)
'dissolute cousin not upper-class' is the wordplay.
'dissolute' is an anagram indicator.
'not' suggests deleting specific letters.
'upper-class' becomes 'u' (similar in meaning).
'cousin' with 'u' removed is 'cosin'.
'cosin' anagrammed gives 'SCION'.
'of' acts as a link.
(Other definitions for scion that I've seen before include "Branch" , "Coins (anag)" , "Issue" , "Offspring" , "Offshoot" .)