Desert or give up (7)
I believe the answer is:
abandon
This clue is a double definition.
'desert' is the first definition.
(synonyms)
'give up' is the second definition.
(synonyms)
'or' is the link.
(Other definitions for abandon that I've seen before include "scrap" , "Walk out on" , "Leave high and dry" , "Junk" , "Desert; give up (action)" .)