Short words many ultimately used for formal greeting (6)
I believe the answer is:
curtsy
'formal greeting' is the definition.
'short words many ultimately' is the wordplay.
'short' becomes 'curt' ('curt' can be a synonym of 'short'**).
'ultimately' indicates one should take the final letters.
The last letters of 'words many' are 'sy'.
'curt'+'sy'='CURTSY'
'used for' is the link.
(Other definitions for curtsy that I've seen before include "Woman's formal greeting" , "Gesture of respect by women" , "Bend the knees in a gesture of respect" , "Bend the knee in respect" , "Kind of respectful bob made by women" .)