'greatly important' is correct and usable in written English. You can use it to emphasize the gravity of a certain situation or decision. For example: "The outcome of this vote is greatly important for the future of our country.".
It was greatly important from a momentum standpoint".
Half of Republican primary goers in Arizona said that a candidate sharing their religious beliefs was somewhat or greatly important to their vote.
Efficient utilization of sunlight is greatly important in photovoltaic systems for high efficiency.
The compaction of an asphalt mixture is greatly important for ensuring durable pavement performance.
'MxR_01' and 'Granada' peach genotypes vary greatly for important traits, such as melting/non-melting, freestone/clingstone, chilling requirement, aromas, and fruit flavour.
Active calls for proposals that bridge the plant-animal-human divides and which integrate evolutionary and ecological theory into understanding the fundamental processes that are shared among infectious diseases would greatly stimulate important translational science.
Memorials and contributions in his honor may be made to either of these organizations and will greatly help their important work.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.