Little appreciation? Test it out! It's most shabby? (8)
I believe the answer is:
tattiest
'most shabby?' is the definition.
('tatty' can be a synonym of 'shabby')
'little appreciation? test it out it's' is the wordplay.
'little' suggests taking the first letters.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'it' becomes 't' (abbreviation. e.g. in 'tis).
The initial letter of 'appreciation' is 'a'.
'a'+'test'+'it'='atestit'
'atestit' anagrammed gives 'tatties'.
'tatties'+'t'='TATTIEST'
(Other definitions for tattiest that I've seen before include "Peeling the most" , "Most shabby and untidy" , "Most moth-eaten" .)