Following rapid ice thinning in the mid-Holocene, Pope Glacier (adjacent to Thwaites Glacier in the Amundsen Sea sector) was at least 30-35 m thinner than present for at least 3 kyr in the mid- to Late Holocene. The timing of the end of this ice lowstand and subsequent rethickening of ice to near its present configuration is poorly constrained. We present five paired ¹⁰Be and ²⁶Al cosmogenic nuclide exposure ages that provide constraints on the timing of this ice sheet readvance. The ages are sourced from samples collected from a moraine <1 km from the grounding line of Pope Glacier on a nunatak between Thwaites and Pope glaciers. To help interpret the new exposure ages, we measure the morphology of the moraine and assess modern ice flow directions to provide an insight into the processes that formed it. We conclude that the moraine is a type of medial moraine and hypothesise that it was formed by englacial thrusting during the advance of a small glacier on the flanks of Mount Murphy approximately 1.4 ± 0.5 ka. We infer that the timing of this glacier advance coincides with the Late Holocene thickening of the adjacent Pope Glacier and speculate that it also coincides with thickening of ice in the wider Amundsen Sea sector. We also note that it coincides with glacier readvances on the Antarctic Peninsula. Our results indicate an ice thickness change from 35 m beneath to 50 m above present levels occurred ~1.4 ka, a scale of ice thickness change that has implications for the interpretation of GPS measurements of ongoing surface uplift used to model the solid Earth’s response to surface mass loading and, in turn, on our ability to understand both past and future ice sheet dynamics.