Either eavesdropped on the conversation or knocked (6)
I believe the answer is:
tapped
This could be a double definition.
'either eavesdropped' is the first definition.
'tapped' can be an answer for 'eavesdropped' (tapping is a kind of eavesdroping). I'm not sure about the 'either' bit.
'knocked' is the second definition.
('tap' can be a synonym of 'knock')
'on the conversation or' acts as a link.
I am not very happy about this link. Some or all of it may belong to one of the definitions.
Can you help me to learn more?
(Other definitions for tapped that I've seen before include "hit" , "Knocked gently" , "Exploited (a resource)" , "Intercepted (a phone)" , "Knocked; exploited" .)