My prefix wants something gone,
My suffix that is now turned on!
My infix is a well known zone,
I am something that is unknown!
Hint:
The last line is part of the riddle.
I think you might be
a question?
My prefix wants something gone,
A quest to rid the world of ... something ..... or (see comments) to find ... something
My suffix that is now turned on!
An ion is charged -> turned on!
My infix is a well known zone,
EST -> Eastern Standard Time (thanks to Mazurka Fahr for the UTC example)
I am something that is unknown!
We ask questions about things that are unknown!
Wait, are you
Goo
My prefix wants something gone,
Go!
My suffix that is now turned on!
O, on a power switch, means off. You just toggled it, so it now on (I).
My infix is a well known zone,
O, for Ozone
I am something that is unknown!
I don't even want to know what most goo is...
I think you might be
x.
My prefix wants something gone,
When you use ex as a prefix, it means you're talking about some former thing which is now gone.
My suffix that is now turned on!
When you use X as a suffix, it can be short for "extra", meaning something special to turn you on.
My infix is a well known zone,
X marks the spot.
I am something that is unknown!
In maths, $x$ is often used for an unknown quantity.
I think you might be
uninvestigated
My prefix wants something gone,
to uninvest Is to withdraw your stake in something.
My suffix that is now turned on!
gated describes a pathway that can be open or closed, on or off.
My infix is a well known zone,
if something has been investigated it is well known
I am something that is unknown!
uninvestigated is unknown
You might be
Outcome
My prefix wants something gone,
Out!
My suffix that is now turned on!
Me! I am excited to solve this riddle
My infix is a well known zone,
UTC, the time zone
I am something that is unknown!
The answer to this riddle
Another stab in the dark
Hint.
My prefix wants something gone,
Hi, to say hello is to want unacquaintedness to be gone
My suffix that is now turned on!
int. is a an abbreviation of internal, the internal connection between the two parties has turned on after their hello
My infix is a well known zone,
in, inside is a well known place
I am something that is unknown!
hint, the hint is hidden by a spoiler tag
Are you...
Antimatter ?
My prefix wants something gone,
Anti could imply being against something (wanting something gone);
My suffix that is now turned on!
ER (emergency room), turned on due to the current situation with COVID;
My infix is a well known zone,
Matt as in Matt Zone, a well know Ohio city councilman.
I am something that is unknown!
Antimatter is still in its early stages of study and dus, still unknown.