Left with a thousand to beat (3)
I believe the answer is:
lam
'beat' is the definition.
(I know that beat is a is a more specific form of the action of lam)
'left with a thousand' is the wordplay.
'left' becomes 'l' (common abbreviation).
'with' is a charade indicator (letters next to each other).
'thousand' becomes 'm' (Roman numeral for a thousand).
'l'+'a'+'m'='LAM'
'to' is the link.
(Other definitions for lam that I've seen before include "Go on the - - , (US sl.)" , "Batter" , "On this, you're fleeing, from the police" , "US criminals commonly escape?" , "Beat hard" .)