There are so many activities and things you can do to improve... it just depends on what area of your writing/roleplaying you want to specifically work on!
That said, there are a few basics that will help regardless of what you're aiming for:
- Read more. Reading from authors you admire and paying attention to how they structure sentences/how they set a scene/how they write action/how they write dialogue/how they make characters/what exactly it is about their writing that you love, can help improve your own writing. Trying to mimic them in order to figure it out is the best way to start out and once you have that down you can branch into your own style of writing.
- Practicing scene writing. I like to do this regularly as a way of practicing my own writing. Basically I'll google an image (it can be anything... whether really simple or really complex) and then work to describe it in as much detail as possible. I'll start with the background (if it's a girl picking flowers in a meadow then I'll start by describing the meadow) and try to be as precise and evocative as possible. From there I work to the girl, her actions, and then any other details I feel might be relevant (mood of the piece, lighting, weather, etc.) Then, I'll get someone I know to read the description and then show them the picture and ask how close their mental image of the scene was compared to the original. Based on their feedback you can get a ton of ideas on areas you might be lacking in and work on it.
Beyond that... it really would help if you were specific on what you're wanting to improve!! I have oodles of things that I've found helpful over the years but I don't want to turn this into a ridiculously long essay if you're just wanting help in specific areas
This is such a broad topic and with so many different approaches many of which are entirely valid, there isn't really one path to point you to. What one person might consider and improvement, another might consider to actually make things worse... Which isn't to say every path will be right, but there are many to help you improve your work.
Still, here a few general tips outside the usual "read, research and practice":
1.Golden Rule of Consistency
The golden rule of consistency is honestly one of the best and most important rules I've learned as a writer. Not only does this rule help improve my writing in general-from characters, to plots, to worldbuilding etc... by making it more solid, interconnected and effective, it can also help generate more content when needed.
The rule has two parts- consistency of internal logic and consistency of consequence. Consistency of internal logic is about following whatever you establish, especially any rules you establish. It also applies to anything established by the setting and by your partner's posts. For an example, if you state that in your character's culture it's normal to be aggressive and violent, your character not being that way requires justification.
Consistency of consequence is an extention of the first rule, that states that things in your work ought to have causes and effects that follow the internal logic established, and complete the rest with common sense. For instance, if you design a setting where everyone can produce light at will with no consequences attached, then any and all busines of producing light is history, you won't see decorated lamps and such, nor any at all for that matter, and people would be more willing to go to dark spaces etc...
2.Know your Style and Preferences
Understanding what your style is like will help you understand what kind of RPs you're best suited for, and through knowing that you may start to get a better sense of what you should focus on as you write. One can't focus on everything at once, one is always going to have flaws and things they aren't as good at. Wanting to improve is definitely a great sentiment, but understanding what you should prioritize for that is likewise very important.
Experiment, and try not to let yourself be discouraged by failure: it is an inevitable part of the process.
3.Holding Back (Moderation and Cooperation)
One of the big lessons I learned as a trading card game player was "just because you CAN do something, doesn't mean you SHOULD". Putting things on a whim isn't always going to be a good idea, not everything which seems cool or funny at a point will necessarily work with your character or story. This goes especially for things in large scale, such as the conflict or a character's power, keeping things more limited makes them more manageable and easier to focus more on the impact those things have than just that they are there.
Long story short, knowing when to dial things back a notch, when not to necessarily go for your wants but knowing to make sacrifices for the sake of a better story, can help greatly improve your writing.
This goes double for RPing, where you also need to take into account your partner's needs. They deserve spotlight as much as you do and will no doubt be happy if you aid them in geting their story in motion, and give genuine interest and cooperation to their work.
4.Learn from your mistakes and the successes and mistakes of others
From trying to figure out the issues and correcting them, to putting your work or ideas out there for feedback, all of these can help you see more specific issues you need to work on. Likewise, engaging with the work of others, their experiences and the like can also help get a fresh perspective on what direction to take your own content.
Hope this helps, best of luck and happy RPing!
Let me know if anything wasn't clear, I'm pretty sleepy as I'm writing this, so I may written something a bit confusing...
In my personal experience, the ways I've improved my writing overall not just roleplaying is by reading novels of different genres and immersing myself in my own stories. There is really no definitive way to improve, it's just personal preference. You have to find out what works for you and what areas you want to improve on. You have to put in the work like you would do anything else in life.