To stare:
a) To look at in a fixed and intense way, usually with your eyes wide open; especially when surprised, frightened, or thinking.
b) To look at, in a fixed and intense way; usually with your eyes wide open; especially when surprised, frightened, or thinking.
Thanks in advance.
My choice from those two would be a) To look at in a fixed and intense way, usually with your eyes wide open; especially when surprised, frightened, or thinking.
For me, the first semi-colon in (b) separates the first and second phrases too much - they need to be combined as they are related.
Personally, I’d probably choose to write it like this:
To look at (especially when surprised, frightened, or thinking) in a fixed and intense way, usually with your eyes wide open.
There are other equally plausible possibilities though.
Hi Beeesneees,
Thanks a lot! I really like yours! 
Would these two sentence be appropriate for that definition?
She stared out of the window.
He stared me up and down.
RtL
‘She stared out of the window’ is okay, but not ‘he stared me up and down’.
Aside from anything else, a stare indicates that you are looking at a single spot, whereas ‘up and down’ indicates a moving focus.
He stared at me.
He looked me up and down.
Hi Beeesneees,
Thanks for this one! I didn’t know it.
RtL