Obsequious subordinates close to tears in Arab country (3-3)
I believe the answer is:
yes-men
'obsequious subordinates' is the definition.
'close to tears in arab country' is the wordplay.
'close to' says to take the final letters (the close of something is the end).
'in' is an insertion indicator.
'arab country' becomes 'yemen' (Yemen is a Middle Eastern country).
The final letter of 'tears' is 's'.
's' inserted inside 'yemen' is 'YES-MEN'.
(Other definitions for yes-men that I've seen before include "lackeys" , "Toadies" , "Sycophants" .)