Die crossing source of Irish river, blooming thing! (13)
I believe the answer is:
passionflower
'blooming thing' is the definition.
(flower which blooms)
'die crossing source of irish river' is the wordplay.
'die' becomes 'pass on' (pass on can mean to die).
'crossing' is an insertion indicator.
'source of' suggests taking the first letters.
'river' becomes 'flower' (a river flows).
The first letter of 'irish' is 'i'.
'passon' going around 'i' is 'passion'.
'passion'+'flower'='PASSIONFLOWER'
(Other definitions for passionflower that I've seen before include "Climbing plant, Passiflora" , "Tropical climbing plant (granadilla)" .)