Prudence doesn't complete the division (6)
I believe the answer is:
thrift
'prudence' is the definition.
(I know that thrift is a type of prudence)
'doesn't complete the division' is the wordplay.
I cannot really see how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found in the answer.
'division' could be 'rift' (I've seen this in another clue) and 'rift' is located in the answer.
A single letter 'h' remains which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for thrift that I've seen before include "Scrimping and scraping" , "Prudence in spending, economical management" , "Careful spending" , "Plant - saving - economy" , "Care in using money" .)