At first seemed half-keen and made out that it would provide a supporting structure (8)
I believe the answer is:
skeleton
'supporting structure' is the definition.
(skeleton is a kind of supporting structure)
'at first seemed half-keen and made out' is the wordplay.
'at first' suggests taking the first letters.
'half' suggests halving the letters.
'and' means one lot of letters go next to another.
'made out' becomes 'leton' (I can't explain this - if you can you should give a lot more credence to this answer).
The first letter of 'seemed' is 's'.
'keen' cut in half is 'ke'.
's'+'ke'+'leton'='SKELETON'
'that it would provide a' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for skeleton that I've seen before include "- key; - staff" , "Reduced to essentials" , "Bony framework" , "gaunt person" , "Framework, outline" .)