Agent, having no money, beginning to rue (6)
I believe the answer is:
broker
'agent' is the definition.
(synonyms)
'having no money beginning to rue' is the wordplay.
'having no money' becomes 'broke' (I've seen this before).
'beginning to' says to take the initial letters.
The first letter of 'rue' is 'r'.
'broke'+'r'='BROKER'
(Other definitions for broker that I've seen before include "See 7" , "Agent paid by commission" , "A dealer in stocks and shares" , "Middleman, dealer" , "intermediary" .)