"foster a new" is correct and can be used in written English.
For example, "She used her position as a mentor to foster a new generation of leaders in her community".
The new initiative to develop young players should foster a new offensive-minded mentality: Scoring.
All these helped foster a new mood of flag-waving patriotism well before the Falklands war.
Immobilizing Mr. Arafat will not foster a new generation of leaders.
But using the FCC's clout to foster a new industry may hold particular appeal for the former internet executive.
Local groups such as BioEnterprise are trying to foster a new generation of health entrepreneurs, with some success.
But is Bashar al-Assad truly, as Syria's official media said, determined to foster a new era of freedom?
So will universal credit foster a new generation of discerning customers looking for a commercially comparable service?
Zia, a true believer, empowered religious societies and political parties in a bid to foster a new national ideology.
Wangechi Mwangi, CEO of Valuraha a company that is trying to foster a new generation of African investors.
In the years that followed, Mr. Liang went on to foster a new national style of architecture that married Chinese and Western motifs.
His aim was to foster a new kind of Weltliteratur, or "world literature," in which far-flung cultures would become more aware of each other.
