Yes, there is.  Here is a link to the post that describes the process: Merge or Combine Activities – Strava Support

Hey @ccnftubadave, I had something similar happen to me recently, where my garmin watch decided to reboot mid-run.  It did save the first bit, but then when it came back to life, I had to start a new run.  I didn't want to have 2 separate activities - so I used an online tool [GOTOES utilities for Strava] that was able to merge the two files together (the tile on the site that says 'combine/repair'). 

You'll need to get the FIT/GPX/TCX file(s) in order to merge them (if you have already synchronized with Strava, you can download the two files from Strava to then upload+merge on the GOTOES site.  Once you upload them and merge, you will get a single (merged) file that you can then upload back to Strava. (you'll likely have to delete the two activities from Strava before you re-upload though, it will see as duplicate otherwise - so keep the two original files saved just in case).

Good luck!

I mean yes GOTOES exists, but wouldn't it be nice to be able to do this in Strava itself? Might cut down on a bit of feed spam as well.

Many times I would like to merge activities, but it's an awful faff to do this via a third party if you are out and about.

Oh, I concur - it would be great to combine directly in Strava.  @willz - have you put this in the Feature Suggestions, then we could all vote for it?   

Just submitted the idea for providing a user friendly way of combining activities.
https://communityhub.strava.com/t5/ideas/combine-activities-afterwards-using-browser-only/idi-p/9574

Please vote.

This was a much used feature of the Endomondo app, which was bought bij Under Armor. Such a shame you now have to spend 5 minutes to fix this. This is something I would like to pay for. 

Try „Track Merger“. You can find it on the App Store. This app allows you to combine multiple tracks. You can even mix GPX, FIT and KML files. Afterwards, you can upload the merged track to your Strava account from within the app.

The reviews for Track Merger are not good and you have to pay for it. What else is available to combine files?

I would love to see a merge function as well. I like to get the heart rate from my Strava on my watch, but I like to view my ride on my phone.  I would either like a merge or be able to display my watch workout on my phone.  The watch is too hard to see while I am riding.