What happens to my investments in Fixed deposit accounts when it matures?

Usually the bank will roll your FD over to a new tenure at the same rate.

fresh fund usually means, the new money is above your previous month balance.

say last mth u have $100k in UOB

u transfer $20k from DBS to UOB, its fresh fund.....

but if u transfer $20k from DBS to UOB and then $20k from another UOB to elsewhere, your overall balance in UOB is still $100k, banks usually take note of that and won't give you the fresh fund promotions...

If the deposit reach maturity, either DBS bank in to you or you go renew FD with them at the prevailing rate...otherwise u can go UOB to do FD... you just need to withdraw out your DBS funds in cash/cheque when apply for UOB FD(if you do not have any account with UOB)