Yes, you can. You can continue at any time when you purchase a MAXQDA license. Just be sure to keep your project file (.mx24).

What happens with my work when the free trial expires? 

All project files you create with a MAXQDA free trial are saved locally on the hard drive of your computer and remain there after the expiration of the free trial. If you reactivate the existing MAXQDA installation with a paid license at a later point, you will also be able to access the previously created files.

You can also move your project to a different computer which has MAXQDA installed on it and continue working from there.

If you just want to read your research work, you have the possibility to install MAXQDA Reader for free.