Computerised application in trouble after millions join up (4,5)
I believe the answer is:
mail merge
'computerised application' is the definition.
'trouble after millions join up' is the wordplay.
'trouble' becomes 'ail' ('ail' can be a synonym of 'trouble').
'after' is a charade indicator (letters next to each other).
'millions' becomes 'm' (abbreviation).
'join up' becomes 'merge'.
'ail' after 'm' is 'mail'.
'mail'+'merge'='MAIL MERGE'
'in' is the link.
(Other definitions for mail merge that I've seen before include "computer program" , "printing software" .)