Just to make clear: You want to take readings continuously during movement of the servo?
In that case: do your reading inside the for loop that moves the servo.
So: move a bit, take a reading, move a bit further...
You need to be more precise.
What did you try (code, schematic), what did you expect, what did you get instead?
Without that info, we cannot help you...
You can not want. You must learn. Then you can do.
When the UltraSonic sensor does this:
trigger pin is pulsed HIGH
transmits a pulse train
receives an echo
No other processing occurs... including "no servo."
What you can do to make it seem "continuous" is to let the SR04 squirt, then move the servo 15 degrees (the angle of the transmitter cone) then squirt again... and repeat. You probably want to move the motors forward a bit, by deciding which is the best time to move (between squirt then servo, or servo then squirt).
This shows that you have not read anything about the HC-SR04 or the servo motor, and ignorantly demand you get what you want. Cows don't make chocolate milk, regardless of how much you want.
Take the advice of everyone and get a little reading done. You will have a much better time when you understand the subject of your project and here on the forum.