The phrase "an ongoing push" is correct and usable in written English.
It can be used to describe a continuous effort or initiative towards achieving a goal or objective.
Example: "The organization has been making an ongoing push to improve community engagement and support."
Alternatives: "a continuous effort" or "a sustained drive".
The update is part of an ongoing push to rejuvenate the ailing brand, led by CEO Marissa Mayer.
The president's failed push for background checks has given way to an ongoing push for immigration reform, and the administration is reportedly planning a sweeping regulatory push on carbon emissions this summer.
They'll be scattered throughout Buenos Aires as part of an ongoing push towards being eco-friendly down there in Argentina.
The rotten defaults could be seen as the start of an ongoing push to get Facebook users sharing more publicly, in response to the rise of Twitter.
Instead, the government rhetoric lends respectability to an ongoing push for recrimination..
The changes are part of an ongoing push to increase penalties around possession that have been unfolding since last year.
I will cheer as you open a new chapter in our ongoing push for a strong and independent CFPB.
On Greece, Juncker says that Greece is aware that it needs to demonstrate "very strong delivery" in the next few weeks (a reference to the ongoing push to find the €11.7bn of cuts needed).
The point is, it's going to take a real concerted and ongoing push from many fronts to break through the floor.
This session was important for all scientists, especially those who are more junior, as a result of the ongoing push to make meaningful contributions to the field.
President Obama traveled to Keene, California, on Monday to designate the home of César E. Chávez as a national monument -- a worthy honor for a key figure in the ongoing push for safe working conditions and fair pay.
