Surveillance post abroad (8)
'surveillance' is the definition.
(stakeout is a kind of surveillance)
'post abroad' is the wordplay.
'post' becomes 'stake' ('stake' can be a synonym of 'post').
'abroad' becomes 'out' (I've seen this before).
'stake'+'out'='STAKEOUT'
(Other definitions for stakeout that I've seen before include "Act of surveillance" , "Put under surveillance - like statue, OK?" , "Police surveillance assignment" , "watch closely" , "Secret surveillance by police" .)
(Another definition for stake-out that I've seen is " Police surveillance operation".)