Knock quietly or finally attempt connection (7)
I believe the answer is:
rapport
'connection' is the definition.
(I've seen this before)
'knock quietly or finally attempt' is the wordplay.
'knock' becomes 'rap' ('rap' can be a synonym of 'knock'**).
'quietly' becomes 'p' (p for piano and quiet).
'finally' says to take the final letters.
The final letter of 'attempt' is 't'.
'rap'+'p'+'or'+'t'='RAPPORT'
(Other definitions for rapport that I've seen before include "communion" , "Empathy" , "Sympathetic understanding" , "Pro rapt with fellow feeling" , "Close and harmonious relationship" .)