。
She put down her needlework and had some tea.
Literal
She [topic-は] needlework [possessive-の] hands [object-を] rested [then-て] tea [object-を] drank.
手を休める (てをやすめる, 'to rest one's hands') is a set phrase for taking a break from manual work. The possessive の links 針仕事 to 手, specifying what kind of work she's pausing from. The て-form connects two sequential events — stopping work, then enjoying tea — in a natural narrative flow. お茶を飲む is the standard way to say 'to have tea,' where お is the polite prefix.