"establish a contact" is correct and usable in written English.
You can use it in a variety of contexts but it generally means forming a connection with someone. For example: "I need to establish a contact with the CEO in order to arrange a meeting."
But still, you must establish a contact of some sort.
As the crisis has unfolded, they have spoken several times, most recently on Sunday night, when Putin agreed to Merkel's proposal to establish a "contact group" to open a dialogue between the two sides.
A projection (arrow) of a mesenchymal cell (MES) is crossing the interface to establish a contact with epithelial (EPI) cells via tunneling nanotubes (arrow head).
Although the bodies of mesenchymal and epithelial stem cells are separated by a striking interface, projections of mesenchymal cells cross it, to establish a contact at the tip of a CD ampulla (Figs. 2a and 3) [48].
Lastly, the system enables local authority to establish a contact with potential event organisers and other small businesses in order to shape the park as a space fit for different types of public events that will also be an important feature for economic viability of the place.
Such a thirst for knowledge goes well beyond simple curiosity, and it can be viewed as an enduring (and sometimes tantalising) interest that views exploration and inquiry as a way to establish a contact with the world outside oneself, as Polanyi put it (Polanyi 1964).
It was while at the Board of Trade that he first established a contact with the Soviet trade mission and with Stalin's shrewd and experienced trade minister, Anastas Mikoyan.
The resolution also established a contact group for intelligence on pirates, which the United States will lead, and suggested several ways to improve the thus far limited legal prosecution of captured pirates.
At the instant this switching device establishes a contact, the capacitor discharges through the primary of the spark coil, and an instantaneous high voltage is delivered to the distributor and thence to the spark plug.
Nevertheless, this woman was content having received a card from the CP early in the process, telling her about the possibility of establishing a contact.
