I got a second chance and I don't want to blow it

Dear forum friends,  if any of you have a thought or a comment, big or small, I'd be so grateful for help. 

At my job I've had a difficult time getting on with one person in particular. I've been there many years but this is the only major conflict I've had, and we had to work on a project together. We're not in the same team.

This other person got another job and is leaving. I don't think I'm the reason or at least not the sole reason. The work I do is very precise and I have a good reputation, although I am known to be very determined and have high standards for myself and not suffer fools gladly. 

Anyway, I started to hate work more every day and today I feel like I got a lifeline. There will be another person doing that job and I have to continue the project.

I have a second chance. I'm autistic but have not come out at work. I'm middle aged. Maybe I'm getting worse.

Any tips to make sure I don't blow it with the new one? They may be located in another country so contact will be 99% by remote working.