Popular flier planned to avoid American in captivity (10)
I believe the answer is:
internment
'captivity' is the definition.
(internment is a kind of captivity)
'popular flier planned to avoid american' is the wordplay.
'popular flier' becomes 'intern' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'planned' becomes 'meant' (I've seen this before).
'to avoid' suggests deleting specific letters.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'meant' with 'a' taken away is 'ment'.
'intern'+'ment'='INTERNMENT'
'in' is the link.
Can you help me to learn more?
(Other definitions for internment that I've seen before include "Precautionary measure" , "Committal" , "Detention" , "Confinement of an enemy national" , "Locking up" .)