Delicacy is not commonly available in dingy housing (6)
I believe the answer is:
dainty
'delicacy' is the definition.
(synonyms)
'not commonly available in dingy housing' is the wordplay.
'not commonly' becomes 'aint' (non-standard version of 'isn't' or 'aren't').
'available in' is an insertion indicator.
'dingy housing' becomes 'dy' (I can't explain this - if you can you should give a lot more credence to this answer).
'aint' placed inside 'dy' is 'DAINTY'.
'is' acts as a link.
Can you help me to learn more?
(Other definitions for dainty that I've seen before include "Twee" , "Delicately small and pretty" , "Choice" , "sensitive" , "Delicate, neat" .)