Hairy case involved somewhere to relax (4,5)
I believe the answer is:
easy chair
'somewhere to relax' is the definition.
I can't judge whether this definition defines the answer.
'hairy case involved' is the wordplay.
'involved' is an anagram indicator (involved can mean confusing or complex).
'hairy'+'case'='hairycase'
'hairycase' with letters rearranged gives 'EASY-CHAIR'.
Can you help me to learn more?
(Other definitions for easy chair that I've seen before include "It's not hard to sit in" , "Common room feature" , "ambitious professor avoids" , "Academic sinecure" , "It's comfortable to sit in - sounds like it" .)