Sheds wiry character erected right away (4-3)
I believe the answer is:
lean-tos
'sheds' is the definition.
(I've seen this before)
'wiry character erected right away' is the wordplay.
'wiry' becomes 'lean' (similar in meaning).
'character' becomes 'T'.
'erected right away' becomes 'os' (I can't explain this - if you can you should believe this answer much more).
'lean'+'t'+'os'='LEAN-TOS'
Can you help me to learn more?
(Other definitions for lean-tos that I've seen before include "outbuildings" , "extensions" .)