Veterans make relationship public, but not at first (3,5)
I believe the answer is:
old hands
'veterans' is the definition.
('old hand' can be a synonym of 'veteran')
'make relationship public but not at first' is the wordplay.
'make relationship public' becomes 'hold hands' (as in a couple holding hands in public).
'but not at first' means to remove the first letter.
'holdhands' with its initial letter taken away is 'OLD HANDS'.
(Other definitions for old hands that I've seen before include "Veterans" , "experienced types" , "Experienced folk" , "Experienced persons" , "Experts" .)