Excited to furtively look over maintenance expenses (6)
I believe the answer is:
upkeep
'maintenance expenses' is the definition.
(upkeep is the cost of keeping something maintained)
'excited to furtively look over' is the wordplay.
'excited' becomes 'up'.
'to furtively look' becomes 'peek'.
'over' shows that the letters should be reversed in order.
'peek' written backwards gives 'keep'.
'up'+'keep'='UPKEEP'
(Other definitions for upkeep that I've seen before include "Peek up at the maintenance" , "Cost of maintaining" , "payments?" , "Running costs" , "Maintenance costs" .)