A cup of tea clutched in her hand

[Bassim]

I am wondering if my sentence is grammatically correct. "Is it correct to begin my sentence as I did, or do I need "with" at the beginning?

A cup of tea clutched in her hand, Hannah paced the room, glancing at her watch all the time, and waiting for her son's return after a night out.

 

[emsr2d2]

You don't need "With" at the start.
I'd change the end to "waiting for her son to return from a/his night out".

The pedant in me says that she can't be both "glancing" at her watch and doing it "all the time". I suggest "glancing repeatedly at her watch".

 

[Skrej]

Or even something like 'glancing frequently', to increase the sense of how often she's looking.