Outdoor run not recording heart rate

If all settings normal but behaviour is irrational there is a progressive hierarchy of  remedies...

First force restart the Watch 

i.e. press and hold both the side button and Digital Crown for at least 10 seconds, then release both buttons when you see the Apple logo. 

 Then, although it may seem irrelevant, while it is restarting Force Restart the paired iphone   Force restart iPhone – Apple Support (UK) 

Test it for a while. If it is still misbehaving... Unpair and set up again

 Unpair and erase your Apple Watch – Apple Support (UK) 

and then 

https://support.apple.com/en-gb/HT204505

You may also want to make sure the software on the watch and iphone  are both up to date to the same level. 

Update your iPhone or iPad - Apple Support

Update your Apple Watch - Apple Support 

If no better you may want to unpair and set up without restoring the backup

If you completed that troubleshooting and the issue is still not resolved, Contact Support. 

 Click here > Contact - Official Apple Support

or phone numbers  

Click here > Contact Apple for support and service - Apple Support

and or Genius Bar Reservation and Apple Support Options - Apple

When you glance at the face during the outdoor run workout, does the heart rate display?

Is the strap a snug fit ie you can squeeze in a pinkie but not a finger between strap and inner wrist?