Yes it will send out new growth in spring. Meanwhile leave the dead looking growth on the plant.

I agree with MG. keeping the dead heads on helps to protect new buds from frost.

Thank you,what a relief !

In mid to late spring, you will see little green shoots making an appearance. You can then cut off the old flower heads down to the topmost shoot on each branch. If bad frosts are forecast, wait till they have passed before doing this