"further ambition" is correct and usable in written English.
It is typically used to express the concept of an ambition that builds on or exceeds an existing one, and is used to signify an increased or more advanced level or degree of ambition. For example, "Having achieved success in his first business venture, Tom set his further ambition on conquering the global market."
What if all the pledges made to date are fully implemented, but there's no further ambition?
Without further ambition, we could see warming of 3C or more.
Obama-era officials who helped craft the UN document point out that the language specifically encourages further ambition while allowing nations to backtrack if necessary, as Japan has done in the wake of the Fukishima nuclear disaster.
And as a one-off, quasi-national-unity ticket, with Lieberman renouncing any further ambition to run for the presidency, a McCain-Lieberman administration wouldn't threaten the continuance of the G.O.P. as a pro-life party.
Momentum for a Taliban Revolution in Pakistan: If the Quetta Shura (Mullah Omar's outfit, the former Islamic Emirate of Afghanistan, now in exile in Pakistan) regained power in Kandahar or Kabul, it would undoubtedly interpret its triumph as a ticket to further ambition in Pakistan.
The strength of the traditional role was that it was filled by a very experienced lawyer with a hinterland who had no further ambition and would therefore fearlessly defend the rule of law and the independence of lawyers and judges against bullying authoritarian cabinet colleagues.
Victories bred further ambitions.
Cheney was not especially popular, and his delicate health ruled out further ambitions.
It has further ambitions to become the first carbon-neutral capital by 2025, to be smoke-free in the same time period, and to serve 90% organic food in all daycares, schools and homes for older people.
Westinghouse filed for Chapter 11 bankruptcy protection in the United States last month, and Toshiba took a loss of more than $6 billion as it wrote down the value of the subsidiary, which it acquired in 2006 to further ambitions to become a world-leading nuclear-energy provider.
However, Mr D'Aloisio has further ambitions for his invention.
