"a fuller understanding" is a correct and usable phrase in written English. You can use it to refer to a more detailed and comprehensive understanding of something. For example, "We need a fuller understanding of the subjects before we make a decision.".
The finding underscores the recognized need for additional research to accelerate a fuller understanding of CTE.
By Tuesday, the authorities said they had a fuller understanding of what had happened.
The missing ingredient was a fuller understanding of language itself.That is still true.
This denies younger readers the background for grasping a fuller understanding of the problem.
Through these "extensive conversations," Mr. Clinton gained a fuller understanding of the "needs" of both sides, Mr. Berger said.
For a fuller understanding of the materials from which plastics are made, see chemistry of industrial polymers.
"Ronald's from those good old days, back in the '70s, man, when people had a fuller understanding," Baker said.
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Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union