JWST imaging of the rich galaxy cluster Abell 2744 at z = 0.308 has been used by the UNCOVER team to construct mosaic images in the NIRCAM filters. The exceptionally deep images in the (F115W, F150W, F200W) bands reveal a large population of unresolved pointlike sources across the field, the vast majority of which are globular clusters (GCs) or Ultra-Compact Dwarfs (UCDs). To the limits of our photometry, more than 10,000 such objects were measured, most of which are in the halos of the five largest A2744 galaxies but which also include GCs around some satellite galaxies and throughout the InterGalactic Medium (IGM). The measured luminosity function covers almost four magnitudes and follows a classic lognormal shape, though the GCLF turnover point still lies fainter than the photometric completeness limit. The colour index (F115W − F200W) in particular covers an intrinsic spread of 0.5 mag, clearly resolving the expected range of GC metallicities. The overall results are consistent with a large, normal GC population seen at a 3.5 Gyr earlier stage of dynamical evolution.