Close to being a miser (4)
I believe the answer is:
near
This clue is a double definition.
'close to' is the first definition.
(close to means nearby)
'being a miser' is the second definition.
(near can mean miserly)
(Other definitions for near that I've seen before include "(Get) close to" , "Close to - stingy - approach" , "unlikely to spend much?" , "Approaching" , "Nigh" .)