From Longman Dictionary of Contemporary Englisheat/drink your filleat/drink your fillold-fashionedFULL to eat or drink as much as you want or need → fill
Examples from the Corpus
eat/drink your fill• I stopped at some blackberry bushes and ate my fill.• Here the nomads water their flocks and the horses drink their fill when the tourists have dismounted.• Menelaus gave them a courteous greeting and bade them eat their fill.• There was still time for Frankie, if he was very quiet and very careful, to eat his fill.• Why were those high-fibre eaters keeping slim even when they were eating their fill? 