Some of the president's team (4)
I believe the answer is:
side
'team' is the definition.
(both can mean a sports team)
'some of the president's' is the wordplay.
'some of' says the answer is hidden in the clue.
'SIDE' is hidden within 'presidents'.
(Other definitions for side that I've seen before include "Airs and graces" , "Wolves, say" , "Face - team" , "Dies for own team" , "Spin given to a ball by striking it off-centre" .)