Yes, in most cases you can, but how it is done depends on the kind of deal and whether the connection you search through is able to carry it.
Airline corporate deals normally come as a code that the airline attaches to a booking connection. If your corporate client has signed its own deal with an airline, the airline usually has to link that code to your connection before anything will show, and the supplier or aggregator you search through has to be able to pass the code along with the search. Once that is set up, the special fare can be made to appear only for that client's own travellers, so your other customers keep seeing normal public fares. Hotels work in a similar way through corporate rate codes, and the same condition applies, the channel you are searching has to support sending that code.
Where your client has signed directly with a hotel or a local supplier and there is no code involved at all, you can usually load those rates yourself as your own contracted inventory and make them visible to that client only. This is often the cleaner route because you control the rate, the cancellation terms and who can see it, without waiting on anyone else. You can also apply client specific discounts or fees on top of normal rates where a full contract is not needed.
Be aware that not every supplier will pass third party corporate codes, and some return the negotiated rate only on certain routes, hotels or dates, so results can look patchy. Before you promise anything to the client, ask each of your suppliers in writing which corporate codes they can pass and on which connection, then run a few test searches under a real traveller profile to confirm the rates actually come back.