Does a single word for "make good use of" exists?
I would suggest utilise
I instinctively spell this ending in -ise, but utilize is the common spelling internationally. I found this useful entry which elaborates further;
For example, "He utilised his experience in order to solve the problem".
to make practical or worthwhile use of
would be another word, but not applicable to all the contexts, it means to take advantage of already existing things in a useful way, while utilize might mean to use it for any needed purpose even if it implies a long process of preparing a new thing from the existing one.