Knock casually yet quickly (7)
I believe the answer is:
rapidly
'quickly' is the definition.
(synonyms)
'knock casually' is the wordplay.
'knock' becomes 'rap' (synonyms).
'casually' becomes 'idly' (I can't justify this - if you can you should give a lot more credence to this answer).
'rap'+'idly'='RAPIDLY'
'yet' is the link.
This may not be correct. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for rapidly that I've seen before include "Fast" , "Speedily" , "With great speed" , "right off the bat" , "Quickly" .)