The phrase "significant importance" is a correct and usable phrase in written English. You can use it to describe the importance of something, for example: "The issue of climate change carries a significant importance for our future.".
Their economic significance means that the ability to identify them rapidly is of significant importance.
"Internationally oriented companies recognise the significant importance of language knowledge at recruitment stage and further into employment.
Lord Bingham placed significant importance on the fact that there are already three safeguards built into the Act.
Perhaps his latest crop, rich in CBD and low in THC, will be the next cannabis plant of significant importance to society.
Phosphorus recycling is also of significant importance.
The performance assessment of such networks is of significant importance.
These results are of significant importance for two reasons.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union