Worker to applaud about second greeting (9)
I believe the answer is:
handclasp
'greeting' is the definition.
(I have seen 'American greeting' mean 'handclasp' so perhaps 'greeting' could also mean 'handclasp')
'worker to applaud about second' is the wordplay.
'worker' becomes 'hand' (hand is a kind of worker).
'to applaud' becomes 'clap' ('clap' can be a synonym of 'applaud').
'about' indicates putting letters inside.
'second' becomes 's' (common abbreviation).
'clap' enclosing 's' is 'clasp'.
'hand'+'clasp'='HANDCLASP'
(Other definitions for handclasp that I've seen before include "greeting in Washington" , "Greeting gesture (in 3 down)" , "American greeting" .)