Make a deep impression and the rest start to hope (4)
I believe the answer is:
etch
'make a deep impression' is the definition.
(I've seen this before)
'and the rest start to hope' is the wordplay.
'and the rest' becomes 'etc' (et cetera).
'start to' indicates taking the first letters.
The initial letter of 'hope' is 'h'.
'etc'+'h'='ETCH'
(Other definitions for etch that I've seen before include "Score deeply" , "Make a deep impression" , "Engrave metal plate using acid" , "Make incisions" , "Delineate" .)