I see several steps in this process, and it starts from self-management.
1. Know & accept that it is OK that we don't get along well with everyone, it happens sometimes.
And this situation also gives a great opportunity for self-reflection and learning what to improve in our soft skills.
2. Don't take it personally (or at least not too much personally :) - I know this step isn't easy, but it is good to be reminded of :)
3. Think of that person ALWAYS with respect. Even though you don't communicate well at the moment, and you have certain differences, the respect has to be there.
When we feel respectful towards others, this shows up, it somehow radiates.
4. Separate the person from their behavior - for example: maybe you don't like their tone of voice, or how they interrupt when others speak, but that is just their behavior.
Keep in mind to respect them as a person and as your colleague. No matter what. And it is okay to disagree with how they behave/communicate. We can always gracefully disagree (as one of my wonderful coach-mentors said).
These are the key elements from self-management part.
Now a few things we can do in interaction with that person:
1. Ask the person for an open conversation, and share your honest thoughts about your communication and what you think could work better.
Once you share, ALWAYS ask the person what they think about what you just said.
Openness and honesty work beautifully, and most people will open up, even more than we think.
Through this feedback conversation find common ways to improve communication.
2. Another option in case the feedback conversation is not fruitful (yeah, this can also happen) - continue to keep in mind to be respectful, professional, clear in your communication.
I think that most of the times what happens in these situations - people loose patience and respect, and then from there it all goes downhill.
Because by adding more negative thoughts & emotions to this situation, it becomes worse to handle and the tension gets bigger.
Hope this is helpful :)