It's tricky to find the best translation in English of the Slovak expression "presadiť sa", because there are so many possibilities (over half a page in my Slovak-English dictionary, including my additions), depending on the specific context. It's not typical for flowers to transplant themselves, so we can ignore that idea, and the sense of swapping places or switching seats does not usually fit the context, I find.

Teachers need to "impose themselves" or "impose their authority" in class. A company can "establish itself" on the market, or "make its mark" with a certain product. New employees can "make their mark" as well, or "push themselves forward" at work, aiming "to be successful" in their career. You can "put yourself across" or "put your ideas across" in a debate or an argument, and one team can "get the upper hand" and "take control" of a match to gain victory. And Happy Valentines, by the way.