My journey ends with request for silence (4)
I believe the answer is:
gosh
'my' is the definition.
(I've seen this before)
'journey ends with request for silence' is the wordplay.
'journey' becomes 'go' (I've seen this in other clues).
'ends with' says to put letters next to each other.
'request for silence' becomes 'sh'.
'go'+'sh'='GOSH'
(Other definitions for gosh that I've seen before include "Exclamation of surprise" , "I'm amazed!" , "expression of surprise" , "Wow!" , "Well I never!" .)