You can have the soft top folded and stored in the car with the hard top fitted. You have to unfasten the rear mount strip that bolts to the rear body panel between the interior and the boot/trunk. Two tie bars (TR part number 625315) attach to the soft top frame and a domed bolt (TR part number 622886) along with a flat washer and a lock washer (TR part numbers 518055 and 518052 respectively) fit through the side mount bracket on the hard top and thread into the tie bar on each side of the car.
There are three different types of soft top boots available. One is your basic soft top boot that is for use with the soft top only. A second style is for use with a hard top when the soft top is stored folded in the car when the hard top is fitted. The third style is supposedly suitable for use with the soft top when the hard top is removed or when the soft top is stored folded in the car when the soft top is fitted. They also vary by chassis number. Seeing that you have a 1976 car, yours would be the latest type for any of the three and all of the styles come in colors to match the interior. I know I have seen the the basic style and the second style, but if I have ever seen one of the third styles, I did not recognize it for what it was.
There are advantages and disadvantages to storing the soft top folded in the car when the hard top is fitted. You pick up extra interior storage room with the soft top out and Triumph used to sell seat inserts for the rear shelf on the TR4 and 4A so that area could be used as an occasional rear seat (hopefully the occasion is a third or fourth birthday because it is tight back there). But if the soft top is out, now you have to come up with a spot to stash it until it is time to fit it again. If you keep the soft top folded and stored in the car when the hard top is fitted, you don't have to worry about coming up with a safe spot to stash the soft top.