"a zeal" is correct and can be used in written English.
You can use it to refer to enthusiasm and energy for something. For example, "He approaches his studies with a zeal that is admirable."
The coach also brought a zeal for the Christian faith.
"She also has a zeal about this," he said.
He discovered a mutual love of cooking and gardening, and a zeal for socializing.
I've always had a zeal for anything that requires a power source.
Canon Simpson did not begin her career with a zeal for ecumenical equality.
For Ms. Sontag, the use of such lines reflects a zeal to capture a historical period.
He had a zeal for playing that was exceptional even among jazz musicians.
They found a camaraderie among other families with a zeal for getting all their letters right.
There are PRs everywhere running things with a zeal that borders on the demented.
"We do have a zeal for laughter in most situations, give or take a dentist".
Turning back to Sky Arts, he says "there is a zeal there.
