Send packing case for outfit around America (4)
I believe the answer is:
oust
'send packing' is the definition.
(I've seen this before)
'case for outfit around america' is the wordplay.
'case for' means to remove the middle letters (the letters which encase the others are used).
'around' means one lot of letters goes inside another.
'america' becomes 'US' (United States).
'outfit' with its middle taken out is 'ot'.
'ot' going around 'us' is 'OUST'.
(Other definitions for oust that I've seen before include "Send packing" , "Put out, say of office" , "Extract" , "Depose" , "Remove or reject from position" .)