I do not think there is any standard word that represents the opposite of the word ‘free’.
There is a simple reason for this. It is (and for millennia has been) in the nature of human transactions that that goods and services are provided for the payment of money in return. Therefore, the default position is that good and services are paid for, so that we don’t need an adjective to tell us so.
So it is the exceptions to this general norm, which we identify with a specific word, ’free’.
The obvious exception of which I am aware is the private school, which is regularly described as ’fee-paying’.
Historically, there have been things that have been free. In Roman times were the famous “bread and circuses”. But these were political measures to bribe the political support or civil quiescence of the urban masses. The kingdoms of islam had vakoufs, charitable foundations which provided a variety of public services at the expense of the royal or powerful. These too were, in effect, gifts of the royal, rich or powerful: charity, if you will. Interestingly, one modern Greek adjective for ’free’ means literally ‘as a gift: dorean - δωρεαν.
In the U.K. since the end of WWII, most aspects of health-care and education (including, till comparatively recently, higher education up to the first degree) have been free to the users.
Dentistry is now widely paid for because of shortage in the supply of dentists. Higher education is part paid for and part free.
Of course, when we call something ‘free’ it is not literally free as air. Someone pays for it. The things I might have are paid for either by me or by the state or by charitable donation (or ‘not for profit’). And the payer, as we are often reminded, is the ‘long suffering tax payer’. And the State, sometimes called the public purse.
For that reason, the contrast between paid for and not paid for is most commonly expressed in terms of, for example, public and private health, education and care. So, if I can afford it, I might for one reason or another decide to have a treatment done privately. That means I pay for it (are my insurance does).
An interesting example is museums. From the 19th century, civic and national museums were key elements of public education, and so were free. Private museums were usually paid for. But no one ever talked about their being free. Nobody thought about paying or not paying: they just went. When under Margaret Thatcher, the great museums had to have paid entry, many declared they ought to be free. But the expression charged or* *paid or fee-paying never arose.
There are words that might do:
paid, charged (for), fee-paying, etc...
But they do not seem to be in common use. I found from a Google search only one use of paid. It was a headline in the Maidenhead Advertiser:
Bucks Council in U-Turn Over Controversial Paid Parking Plan for Marlow.
But of course headline writers are seeking to minimise the number of words.