You could try refreshing your stats by going to your profile and clicking Refresh Stats on the right-hand side.

Unfortunately, what’s more likely is that Strava didn’t grant you a PR because it didn’t quite record 10 kilometers, which is approximately 6.21371 miles, whereas your screenshot shows a distance of 6.20 miles.

There have been many, many discussions on this topic over the years, including 

I wouldn’t let that detract you from the achievement, though, regardless of what the app thinks: Congrats on the amazing time! What a way to end/start the year.

Going forward, Strava users often recommend running just a little farther, to make sure the app records your achievement, if you believe you scored a personal best. It’s unfortunate, and I know it doesn’t solve your current issue; but that’s the state of things.

I agree with ​@zecanard that the most likely reason it isn’t showing up is that you did not quite go far enough to count as a 10k.  As they mentioned, lots of people have the same issue.  It happens a lot when people do a race and the distance is either slightly short or their GPS tracking is just a fraction off and comes up short and people typically don’t or can’t run past the finish line to ensure they cover a little extra to be safe.  

Two things I can think of that might help you though with this effort.  The first is just speculation and I don’t know if it will actually show up on the Best Effort list.  You can add a manual entry with the distance (enter 6.25 or 6.3 miles just to be safe) and time of this effort.  I don’t know for sure if the best effort stat will pull from manual entries or if it is limited to actual GPS recordings, but might be worth a try.  You could make that private so it doesn’t show up as a duplicate on your feed.  Another option would be to just enter your time from this effort into your PR list.  In your stats, you have two lists of times, Best Efforts and PRs.  Best efforts are pulled from your activities, but the PRs are ones you enter yourself and could come from any other activity that may or may not be recorded in Strava.  You can link that to a race result as well if you wanted.  This would at least show that time as your PR in the 10k distance.  See this link for details: All-Time PRs – Strava Support

To add, yet try the Correct Distance feature (open the activity on the Strava website - it's not an option in the mobile app! - then in the menu on the left, click the three dots, and then Correct Distance). That will recalculate the activity based on the map data and if you're lucky, it will give you the 10k

Also if you are looking at PR and not best efforts, you can just edit it and point it back to this activity. From the website click on your profile and then click ‘Add PR’, you can edit the existing ones from here.

The idea of the PR section is to have a time verified to a race, on my profile some of these are slower than my actual best effort eg my half marathon was faster in a training run than an official race!

That’s the idea but you can use it how you like as its manually done:

https://support.strava.com/hc/en-us/articles/216918487-All-Time-PRs#:~:text=All%2Dtime%20Personal%20Records%20(PRs,race%20results%20and%20Strava%20activities.