Greeting Republican, a Kennedy turned aside (7)
I believe the answer is:
averted
'turned aside' is the definition.
(I've seen this before)
'greeting republican a kennedy' is the wordplay.
'greeting' becomes 'ave' (Latin greeting).
'republican' becomes 'R' (abbreviation).
'a kennedy' becomes 'ted' (US senator Ted Kennedy, 1932-2009).
'ave'+'r'+'ted'='AVERTED'
(Other definitions for averted that I've seen before include "Prevented, headed off" , "Turned away (one's eyes)" , "Staved off" , "Turned aside or deflected" , "avoided" .)