Become worn down, or endure topic of desultory conversation (7)
I believe the answer is:
weather
'endure topic of desultory conversation' is the definition.
'weather' can be an answer for 'endure' (synonyms). I am not certain of the 'topic of desultory conversation' bit.
'become worn down' is the wordplay.
I cannot quite understand how this works, but
'down' could be 'eat' (I've seen this in other clues) and 'eat' is located in the answer.
This explanation may well be incorrect...
'or' acts as a link.
Can you help me to learn more?
(Other definitions for weather that I've seen before include "ride out" , "Climatic conditions" , "Conditions outside; survive (crisis)" , "Survive (ordeal); be worn away naturally" , "Local atmospheric conditions" .)