If you keep the same license, then just add your name to it. Say it was this original license https://github.com/mauro3/Parameters.jl/blob/master/LICENSE.md, then change it to something like:
Copyright (c): Mauro Werder (2015-2018), Han Hasse (2019)
If it is not the same type of license (or no license, or no open source license), then it’s more tricky.