Busy filling the bottom drawer (7)
I believe the answer is:
engaged
'busy' is the definition.
(I know that busy can be written as engaged)
'filling the bottom drawer' is the wordplay.
'filling' means one lot of letters goes inside another.
'the bottom' becomes 'end' (I've seen this in other clues).
'drawer' becomes 'gage' (I can't justify this - if you can you should believe this answer much more).
'end' placed around 'gage' is 'ENGAGED'.
Can you help me to learn more?
(Other definitions for engaged that I've seen before include "Spoken for" , "as a result of a proposal" , "Taken on - betrothed" , "Fully committed - to get married?" , "Absorbed" .)