Demanding second appointment, finally call hospital department (9)
I believe the answer is:
stringent
'demanding' is the definition.
(similar in meaning)
'second appointment finally call hospital department' is the wordplay.
'second' becomes 's' (common abbreviation).
'finally' indicates one should take the final letters.
'call' becomes 'ring' (telephone call).
'hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
The final letter of 'appointment' is 't'.
's'+'t'+'ring'+'ent'='STRINGENT'
(Other definitions for stringent that I've seen before include "Severe, rigorous, attention to rules say" , "Strict, rigorous" , "Requiring strict adherence to detail" , "Tough" , "Demanding, inflexible" .)