The morning's breaking over source of Snake River (6)
I believe the answer is:
thames
'river' is the definition.
(English river)
'the morning's breaking over source of snake' is the wordplay.
'morning' becomes 'am' (as in 12:00 AM).
'breaking' is an insertion indicator.
'over' is a charade indicator (letters next to each other).
'source of' indicates taking the first letters (the start - or source - of the word).
The first letter of 'snake' is 's'.
'the' placed around 'am' is 'thame'.
'thame'+'s'='THAMES'
(Other definitions for thames that I've seen before include "capital banker" , "The Isis at Oxford" , "Capital's river" , "One going to live abroad" , "River at Lechlade" .)