Stick around Midway, a Pacific island (4)
I believe the answer is:
guam
'a pacific island' is the definition.
(I've seen this before)
'stick around midway' is the wordplay.
'stick' becomes 'gum' (I've seen this before).
'around' is an insertion indicator.
'midway' becomes 'a' (I am not sure about this - if you are sure you should believe this answer much more).
'gum' enclosing 'a' is 'GUAM'.
Can you help me to learn more?
(Other definitions for guam that I've seen before include "North Pacific island, base for the US navy and air force" , "Largest of the Mariana Islands" , "place in the Marianas" , "Island in the West Pacific" , "NW Pacific island with large US base" .)