Money starts to cause annoying shortage here (4)
I believe the answer is:
cash
'money' is the definition.
(thesaurus)
'starts to cause annoying shortage here' is the wordplay.
'starts to' suggests taking the first letters.
The first letters of 'cause annoying shortage here' is 'CASH'.
(Other definitions for cash that I've seen before include "Money in the form of notes and coins" , "Till" , "Spondulicks" , "Ready money" , "Singer Johnny, d. 2003" .)