Lived on delta, having acquired some skin damage (5)
I believe the answer is:
dwelt
'lived' is the definition.
(I've seen this in another clue)
'delta having acquired some skin damage' is the wordplay.
'delta' becomes 'd' (phonetic alphabet: alpha, bravo, charlie etc.).
'having' is a charade indicator (letters next to each other).
'acquired some skin damage' becomes 'welt' (I can't explain this - if you can you should give a lot more credence to this answer).
'd'+'welt'='DWELT'
'on' is the link.
Can you help me to learn more?
(Other definitions for dwelt that I've seen before include "lodged" , "Had house" , "Inhabited" , "Remained" , "Spoke at length" .)