The phrase "a sharp escalation in" is correct and usable in written English.
It can be used to describe a sudden and significant increase in something, such as a situation, trend, or issue.
Example: "There has been a sharp escalation in the number of reported cases over the past week."
Alternatives: "a significant rise in" or "a steep increase in".
His letter represents a sharp escalation in the row between Miliband and the Mail group.
The attack, in a speech Mr. McCain is to give today, marks a sharp escalation in the war of words between two of the leading Republican presidential contenders.
By evening, Israel had issued a stern warning that it was examining all possible responses, signaling the potential for a sharp escalation in the area.
It was a sharp escalation in an already worsening trend.Another bad omen was the resignation of Mohamed ElBaradei, Egypt's acting vice-president.
Visiting in July she found a sharp escalation in the number of mothers on suicide watch and babies confined to small metal containers, where they cannot learn to crawl or walk.
Other figures from NHS England, which reveal a sharp escalation in other problems over the festive period, especially in the week including and just after the new year, indicate the service was on the brink of a winter crisis.
After months of growing tension between the government and foreign security contractors, the decision marks a sharp escalation into public action by the Afghan authorities.
The report comes after a sharp escalation of violence in Afghanistan, where more American troops died in August than in any month since the beginning of the war.
By providing warplanes and, in the case of the United States, logistical and intelligence support, both countries are playing an important, enabling role in the operation, which in recent weeks has contributed to a sharp escalation of violence in Yemen.
Activists reported a sharp escalation of violence in the last two days, saying at least 17 people were killed in one neighborhood alone in troubled Homs, the city that has become a focal point for concerns about Syria's slide into civil war.
Over the weekend the Russian foreign ministry issued a statement condemning what it described as a sharp escalation of violence in eastern Ukraine, where pro-Russian militants have declared "people's republics" in Donetsk and Luhansk, following an unofficial referendum in favour of independence.
