"further aspiration" is correct and usable in written English.
You can use it to refer to an additional ambition or goal, beyond what has already been achieved. For example, "Her further aspiration was to attend an Ivy League university."
Certainly, jazz, as a self-contained art form, has no further aspiration than self-improvement.
A further aspiration of the 10 10 campaign is to influence international talks in Copenhagen in December at which a treaty to tackle global warming will be thrashed out.
She rebranded Ray's coffee shop toward the end of season five but now seems intent on no further aspiration.
She rebranded Ray's coffee shop toward the end of season five but now seems intent on no further aspiration.
He was treated by performing an intranasal ethmoidectomy and further aspiration.
The recurrence of clinical symptoms over ensuing months prompted further aspiration and biopsy of a cervical abscess and underlying lymph nodes.
"He's outside that goldfish bowl and if he has got further aspirations of coaching Wales in the near future then I think it might be the right move for him".
Any talk of further aspirations plants the seed that they'll eventually need to replace you..
This further creates aspiration and desire in the consumer.
He told the conference hall: "In the next parliament, I want us to go further; our aspiration should be that someone working full time on the minimum wage should pay no income tax at all.
Instead he placed an emphasis on how to push ahead with the Lib Dem income tax policy: "In the next parliament, I want us to go further; our aspiration should be that someone working full time on the minimum wage should pay no income tax at all.
