No. As said earlier, a trademark represents a brand and protects it against consumer confusions. Suppose you want to use the logo of a company or a famous celebrities image in your design. Depending on how you use, it could lead to trademark infringement. Or, it can lead consumers to think that the t-shirts you sell are official merchandise and the brand is selling it since you referenced it in your design.
Unless you are legally entitled or worked out a deal with the brand of the specific trademark, you cannot use someone else’s trademark. It is trademark infringement.
Some countries allow for trademark fair use by modifying some aspects of a design. But it is not the solution. We recommend you to use only the original concept.
We recommend you to contact an attorney if you want a legal resolution regarding trademark use.