Die by water, having fallen crossing river (5)
I believe the answer is:
drown
'die by water' is the definition.
'drown' can be an answer for 'die' (drowning is a kind of diing). I'm not sure about the 'by water' bit.
'fallen crossing river' is the wordplay.
'fallen' becomes 'down' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'crossing' indicates putting letters inside (to cross can mean to go over or around).
'river' becomes 'r' (abbreviation for river).
'down' going around 'r' is 'DROWN'.
'having' acts as a link.
Can you help me to learn more?
(Other definitions for drown that I've seen before include "Flood (an area)" , "Completely conceal" , "Die in water" , "Perish in water" , "Die from submersion in liquid" .)