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' suggests the final letters (the 'close' to the word).
'in' indicates putting letters inside.
'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" .)