"a little gap between" is grammatically correct and can be used in written English.
It is used to describe a small space or distance between two objects or concepts. Example: There was a little gap between the shelves, just enough for a small book to fit through.
The small-scale self-heating experiments show that there is a little gap between the Critical Ambient Temperature (CAT) of sodium dithionite and thiourea dioxide.
"Sadly, a hollowed part of the trunk of that tree lying on the ground was filled with concrete in the 1960s, and a little gap between the concrete and wood has left space for organisms to grow, causing rot.
Just an FYI: We're in a little gap between issues right now, so we're posting a few "classic" articles from the magazine that haven't been available on the site since they were published in the Vice Guide to Sex and Drugs and Rock and Roll.
There should be a little gap between your head and palms.
Avoid your cuticles, and leave a little gap between the nail and skin.
If your team barely missed its targets, bring everything in, perhaps showing a tiny little gap between your thumb and forefinger.
This is a society with little gap between public and private.
Tom Pietrzak, the driver, said that for highway driving, he adjusts the distance between the trailer and the cab to just a few inches so that there is little gap between the back of the fairing and the front of the trailer.
After viewing The Fifth Estate, David Leigh, one of the writers on whose account it was based, agreed and stated that one of the movie's problems was that "It falls into that little gap between 'Oh we know all that, we remember it!' and 'This is history, therefore interesting.'".
However, there is very little gap between what girls and boys can learn, and herein lies the rub.
