"subtly push" is a correct and usable phrase in written English.
It means to gently nudge or influence someone or something in a subtle manner. Example: She subtly pushed her ideas during the meeting without being too forceful. or The company subtly pushed their new product by offering it as a limited time offer.
Is this something you're discussing explicitly, the kinds of roles you're looking to embrace, or are you hoping to just subtly push these kinds of dynamics?
Now, the outcomes of all three appear inextricably linked, as a host of political players, all with their own forms of leverage, subtly push competing agendas and guard their own interests.
Knowing your partner is achieving additional success can subtly push you to work harder, Bobby said.
That could subtly push publishers away from covering some of the more devisive topics in the world from war to social justice because they know they can't earn money from it.
However, he agreed that situational factors can subtly push people toward cooperation or self-interest.
Between the two outlets, Putin is able to subtly push a disinformation campaign inside NATO's borders.
Another theory, denied by the White House, was that Mr. Cheney was subtly pushing his boss.
Erdogan stopped kissing Erbakan's hand because it struck him as retrograde, and he subtly pushed for greater democracy within the party and for broader outreach.
On the other hand, Rockwell's reviews may have subtly pushed The Times's arts coverage in a looser, more colloquial direction.
The latest issue may have had particular resonance with Facebook users because the company has been reeling from a series of privacy controversies, in part because it has been subtly pushing users to share data more publicly.
It is related to a concept sometimes called "libertarian paternalism" — subtly pushing people to make rational choices — that has been applied in other fields, like checkoffs for organ donations on driver's license applications.
