Hesitantly drops this in an orderly fashion (6)
I believe the answer is:
neatly
'hesitantly drops this in' is the definition.
Both the answer and definition are adverbs. Maybe you can see a link between them that I can't see?
'an orderly fashion' is the wordplay.
'an orderly' becomes 'neat' (I've seen this before).
'fashion' becomes 'ly' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'neat'+'ly'='NEATLY'
Can you help me to learn more?
(Other definitions for neatly that I've seen before include "Tidily and cleanly" , "'Tidily, trimly (6)'" , "In a tidy manner" , "In a tidy way" , "nicely" .)