Sometimes moving to an agile approach can be hard. For example, it may seem like some parts of an agile framework would work in your context, but others clearly won't. Alternatively, it may be that you can follow an agile framework, but there are still things your organisation needs you to do on top of what the framework says. Producing Gannt chart plans for example, or monthly RAG status reports, or committing to a fixed scope by a fixed delivery date.
When this happens, people do often ask whether they can blend 'waterfall'(traditional project management) and agile approaches in their work.
The short and literal answer is that technically speaking of course they can. Just like you can mix any food ingredients you like with any other ingredients when cooking a meal. The bigger question though is whether doing so is a good idea? In both cases, the answer is probably not.
Whilst you can blend watefall and agile approaches, very often doing so leads to conflict between the two, and sub-optimal outcomes overall.
For example, those Gantt charts you're asked to produce. How much value do they add, truthfully speaking. How quickly do they go out of date? Would anything be significantly different if they weren't produced? One of the principles of the agile manifesto states 'Simplicity - the art of maximising the amount of work not done - is essential'. So if you're mixing waterfall with agile, are you really maximising the amount of work not done? Straight away, the two approaches conflict.
You get even bigger problems when you try to mix waterfall approaches like delivering a fixed scope by a fixed date with agile approaches. Agile is about 'responding to change over following a plan', so if your scope and timeline are fixed, how can you respond to change? In reality, doing something like this just leads to teams standing up next to whiteboards covered in sticky notes, wondering why they're being told to be agile when they have no ability to change anything.
So yes, you can mix waterfall and agile if you want. But the more you do so, the more likely it is that the two approaches will conflict with each other, causing you to waste time and effort that could have been better spent doing one approach well.