The phrase "an already intense" is correct and usable in written English.
It can be used to describe a situation or feeling that is already strong or heightened before an additional factor is introduced.
Example: "The discussion became even more heated in an already intense debate about climate change."
Alternatives: "a previously intense" or "an already heightened".
In an already intense family, the tie between Tony and his mother had been exceptionally intense.
The riots have fuelled an already intense debate in the Labour high command about how to oppose Mr Cameron.
"The European Commission has thrown a hand grenade into an already intense debate about the U.K.'s continued E.U. membership," he said.
But the choice is also likely to add heat to an already intense debate about the role biotechnology can play in combating world hunger.
That protest added to an already intense media debate over the rise of a low-wage economy in America as the country's economy struggles to recover.
Chelsea have already played 40 games this term, having flown to Japan for the Club World Cup final before Christmas, and the replay against Brentford on Sunday 18 February is an unwelcome addition to an already intense fixture list.
Critics say online cramming adds to a student's already intense schedule.
Expanding existing streets is often not an option due to already intense development and the severe limitation of available land.
When Rosberg blocked Hamilton's attempt to secure pole here a year ago a rivalry that was already intense became something darker.
And even though receiver Wayne Chrebet said the Jets would like to "save some face" after their dismal 41-28 loss to the Giants in Week 13 of the regular season, the real purpose of this game is not to add any more fuel to a rivalry that is already intense.
Given the projected increases over the next decades in the world's population, especially in developing countries where pressure on land and water is already intense, a key challenge facing the international community is to ensure food security for present and future generations, while protecting the natural resource base on which we all depend.
