Worn out, quiet cat dropping head (6)
I believe the answer is:
shabby
'worn' is the definition.
(similar in meaning)
'out quiet cat dropping head' is the wordplay.
'out quiet' becomes 'sh' (I am not sure about the 'out' bit.).
'cat' becomes 'tabby' (tabby is a kind of cat).
'dropping head' means to remove the first letter.
'tabby' with its first letter removed is 'abby'.
'sh'+'abby'='SHABBY'
Can you help me to learn more?
(Other definitions for shabby that I've seen before include "Old and worn - mean" , "Dingy - dirty" , "Worn and run-down, like clothes" , "Threadbare - despicable" , "'Scruffy, tattered (6)'" .)