Rush to get a letter to press (5)
I believe the answer is:
surge
'rush' is the definition.
(synonyms)
'get a letter to press' is the wordplay.
'get' means one lot of letters go next to another.
'a letter' becomes 's' ().
'to press' becomes 'urge' (press can mean to urge or encourage).
's' next to 'urge' is 'SURGE'.
'to' is the link.
(Other definitions for surge that I've seen before include "Sudden powerful increase" , "Rolling swell of the sea" , "Sudden large increase" , "Sudden increase, gush" , "Jerk" .)