This work presents the results from extending the long-term monitoring program of stellar motions within the Galactic Center to include stars with separations of 2–7 arcsec from the compact radio source, Sgr A*. In comparison to the well studied inner 2 arcsec, a longer baseline in time is required to study these stars. With 17 years of data, a sufficient number of positions along the orbits of these outer stars can now be measured. This was achieved by designing a source finder to track the positions of ∼2000 stars in NACO/VLT adaptive-optics-assisted images of the Galactic Center from 2002 to 2019. Of the studied stars, 54 exhibit significant accelerations toward Sgr A*, most of which have separations of between 2 and 3 arcsec from the black hole. A further 20 of these stars have measurable radial velocities from SINFONI/VLT stellar spectra, which allows for the calculation of the orbital elements for these stars, thus increasing the number of known orbits in the Galactic Center by ∼40%. With orbits, we can consider which structural features within the Galactic Center nuclear star cluster these stars belong to. Most of the stars have orbital solutions that are consistent with the known clockwise rotating disk feature. Further, by employing Monte Carlo sampling for stars without radial velocity measurements, we show that many stars have a subset of possible orbits that are consistent with one of the known disk features within the Galactic Center.