Drunk and a rich web designer (8)
I believe the answer is:
arachnid
'web designer' is the definition.
(I've seen this before)
'drunk and a rich' is the wordplay.
'drunk' is an anagram indicator.
'and'+'a'+'rich'='andarich'
'andarich' with letters rearranged gives 'ARACHNID'.
(Other definitions for arachnid that I've seen before include "Class of animals including spiders and scorpions" , "Spider, mite, tick etc.; had in car (anag.)" , "Mite or tick, for example" , "Animal class including spider, scorpion etc" , "Incy Wincy Spider, say" .)