We searched for z \gtrsim 7 Lyman-break galaxies ( LBGs ) in the optical-to-mid-infrared Hubble Frontier Field and associated parallel field observations of the strong-lensing cluster MACS J0416 - 2403 . We discovered 22 candidates , of which six lie at z \gtrsim 9 and one lies at z \gtrsim 10 . Based on the Hubble and Spitzer photometry , all have secure photometric redshifts and a negligible probability of being at lower redshifts , according to their peak probability ratios , \Re . This substantial increase in the number of known high-redshift galaxies allows a solid determination of the luminosity function at z \gtrsim 8 . The number of high-z candidates in the parallel field is considerably higher than that in the Abell 2744 parallel field . Our candidates have median stellar masses of log ( M _ { * } ) \sim 8.40 ^ { +0.55 } _ { -0.31 } M _ { \odot } , SFRs of \sim 1.6 ^ { +0.5 } _ { -0.4 } M _ { \odot } yr ^ { -1 } , and SFR-weighted ages of \lesssim 310 ^ { +70 } _ { -140 } Myr . Finally , we are able to put strong constraints on the z = 7 , 8 , 9 and 10 luminosity functions . One of the objects in the cluster field is a z \simeq 10 candidate , with a magnification of \mu \sim 20 \pm 13 . This object is likely the faintest z \sim 10 object known to date , allowing a first look into the extreme faint-end ( L \sim 0.04 L ^ { * } ) of the z \sim 10 luminosity function .