Query expansion has been proved to be effective in improving recall and precision of first-stage retrievers, and yet its influence on a complicated, state-of-the-art cross-encoder ranker remains under-explored. We first show that directly applying the expansion techniques in the current literature to state-of-the-art neural rankers can result in deteriorated zero-shot performance. To this end, we propose GFF, a pipeline that includes a large language model and a neural ranker, to Generate, Filter, and Fuse query expansions more effectively in order to improve the zero-shot ranking metrics such as nDCG@10. Specifically, GFF first calls an instruction-following language model to generate query-related keywords through a reasoning chain. Leveraging self-consistency and reciprocal rank weighting, GFF further filters and combines the ranking results of each expanded query dynamically. By utilizing this pipeline, we show that GFF can improve the zero-shot nDCG@10 on BEIR and TREC DL 2019/2020. We also analyze different modelling choices in the GFF pipeline and shed light on the future directions in query expansion for zero-shot neural rankers.