From Longman Dictionary of Contemporary Englishbuild up to something phrasal verbINTRODUCEto prepare for a particular moment or event I could tell she was building up to some kind of announcement. → build→ See Verb table
Examples from the Corpus
build up to • Gradually, he built up to a mile a day, roughly five days a week.• Magona has a surer touch when narrating the sweep of history that builds up to create inevitable results.• If this was not filtered out of the cabin supply then the CO2 would slowly build up to dangerous proportions.• The surface could be built up to some extent by the application of thick and successive layers.• It had built up to such a level that truth was hidden pretty deep. 