Here are my observation when taking a portrait with blurry background outdoors in ambient light and adding a flash. I used a Profoto A1.
Most flashes have TTL (automatic light exposure Thru The Lens) and HSS (High Speed Sync allows flash sync at higher shutter speeds) but few uses them so I had to try to see what difference they do. I also used some simple accessories to shape light.
Model: Josefine Forsberg

Picture 1:
Ambient light and no flash
Settings: ISO 100, f2.8, 1/800s
Good exposure on talent but the sky is burnt out and boring.

Picture 2:
Ambient light and no flash
Settings: ISO 100, f2.8, 1/2500s
Here I bumped up the shutter speed to get the sky blue but then the talent is underexposed. Background is still blurry.

Picture 3:
Flash added
Settings: ISO 100, f14, 1/200s
Now I added a flash which forces the camera shutter speed to 1/200s so the aperture needs to be bumped up to f14. Good exposure on talent and background has blue sky but the background is sharper due to aperture f14. There is a typical “flashy” feel to the picture with highlights in the face.

Picture 4:
HSS turned on
Settings: ISO 100, f2.8, 1/2000
With High Speed Sync I can sync the flash even with faster shutter speeds. Now I get a good exposure on talent and the background is blurry with blue sky.

Picture 5
HSS flash with a dome
Settings: ISO 320, f2.8, 1/2000
I added an accessory to diffuse the light on talent keeping the background blurry with blue sky. Very natural feeling to the light and the sun created a halo effect around the talent. The diffusor required more light so I bumped up the ISO.

Picture 6:
HSS flash, Profoto A1 with Soft Bounce.
Settings: ISO 320, f2.8, 1/3200
Softer light on talent and background is blurry with blue sky. This did not require as much light as the diffusor so I bumped up the shutter speed. Alternatively I could have taken down the ISO to 100.

As always when you work with light there is no right or wrong. It’s all about what mood or feeling the photographer wants to create but it’s good to know what happens when you use specific settings or functions so that you faster can create what you want smiley