Source of electrons: gamble successfully handled, picked up over a year (4,5)
I believe the answer is:
beta decay
'source of electrons' is the definition.
'gamble successfully handled picked up over a year' is the wordplay.
'gamble' becomes 'bet' (betting is a kind of gambling**).
'successfully handled' becomes 'aced'.
'picked up' says the letters should be written backwards.
'over' indicates putting letters inside.
'year' becomes 'y'.
'aced' written backwards gives 'deca'.
'bet'+'deca'='betdeca'
'betdeca' enclosing 'a' is 'betadeca'.
'betadeca'+'y'='BETA DECAY'
(Another definition for beta decay that I've seen is " particle emission".)