Cut costs, bound to save money, initially (5)
I believe the answer is:
skimp
'cut costs bound to save money initially' is the definition.
I can't tell whether this definition defines the answer.
'bound to save money initially' is the wordplay.
'bound' becomes 'skip' (I've seen this before).
'to save' means one lot of letters goes inside another.
'initially' indicates taking the first letters.
The first letter of 'money' is 'm'.
'skip' going around 'm' is 'SKIMP'.
Can you help me to learn more?
(Other definitions for skimp that I've seen before include "Expend less in an attempt to economise" , "Be niggardly" , "Stint in order to economise" , "hasty" , "Deal with superficially" .)