Turn up to either building, though not hospital (9)
I believe the answer is:
pirouette
'turn' is the definition.
(I know that pirouette is a type of pivot)
I can't explain the remainder of the clue.
(Other definitions for pirouette that I've seen before include "A dancer's spinning movement on tiptoe" , "Tore up tie (anag) - spin" , "bit of dancing" , "Spin on one foot" , "Take turn on foot" .)