Brief trip leading to deficit (9)
I believe the answer is:
shortfall
'deficit' is the definition.
('shortfall' can be a synonym of 'deficit')
'brief trip leading' is the wordplay.
'brief' becomes 'short' ('short' can be a synonym of 'brief').
'trip' becomes 'fall' (fall is a kind of trip).
'leading' says to put letters next to each other.
'short'+'fall'='SHORTFALL'
'to' is the link.
(Other definitions for shortfall that I've seen before include "what we're lacking" , "Not enough money" , "lack" , "Not quite what's expected" , "Deficiency" .)