Hospital teas prepared in great speed (5)
I believe the answer is:
haste
'great speed' is the definition.
'hospital teas prepared in' is the wordplay.
'hospital' becomes 'h' (**).
'prepared' indicates an anagram.
'in' indicates putting letters inside.
'teas' anagrammed gives 'aste'.
'h' placed inside 'aste' is 'HASTE'.
(Other definitions for haste that I've seen before include "''More . . . . ., less speed'' (5)" , "Promptitude" , "Urgent hurry" , "More of this can slow you up!" , "Hurry, urgency" .)