Hair-splitter set up shop and it's rubbish (7)
I believe the answer is:
sophist
'hair-splitter set up' is the definition.
I can't judge whether this definition defines the answer.
'shop and it's rubbish' is the wordplay.
'and' means one lot of letters go next to another.
'rubbish' indicates anagramming the letters (a poor quality or rubbish spelling of the letters).
'shop'+'its'='shopits'
'shopits' with letters rearranged gives 'SOPHIST'.
Can you help me to learn more?
(Other definitions for sophist that I've seen before include "Clever but fallacious reasoner" , "One given to specious reasoning" , "One who uses clever but false argument" , "One using clever but wrong arguments" , "One using clever but fallacious arguments" .)