Rush to get a letter to press (5)
I believe the answer is:
surge
'rush' is the definition.
(I know that rush can be written as surge)
'a letter to press' is the wordplay.
'a letter' becomes 's' ().
'to press' becomes 'urge' (synonyms).
's'+'urge'='SURGE'
'to get' acts as a 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" .)