Author mostly concerned with having no luxuries (7)
I believe the answer is:
austere
'having no luxuries' is the definition.
I can't tell whether this defines the answer.
'author mostly concerned with' is the wordplay.
I cannot quite see how this works, but
'concerned with' could be 're' (re can mean regarding, concerning) and 're' is present in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for austere that I've seen before include "Grim -- a US tree (anag)" , "'Spartan, simple (7)'" , "Harsh" , "Stern, grave" , "Stern or very plain" .)