Obvious regret, dropping resistance to second proposal (8)
I believe the answer is:
overture
'proposal' is the definition.
(overture is a kind of proposal)
'obvious regret' is the wordplay.
'obvious' becomes 'overt' (similar in meaning).
'regret' becomes 'ure' (I can't justify this - if you can you should believe this answer much more).
'overt'+'ure'='OVERTURE'
'dropping resistance to second' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for overture that I've seen before include "Item of music" , "Musical prelude to opera or ballet" , "Orchestral prelude to opera" , "Orchestral introduction to an opera" , "Friendly approach or orchestral prelude" .)