Persuasive speech from rector, I recollected, about hospital (8)
I believe the answer is:
rhetoric
'persuasive speech' is the definition.
(I've seen this before)
'rector i recollected about hospital' is the wordplay.
'recollected' indicates anagramming the letters (letters recollected and rearranged).
'about' is an insertion indicator.
'hospital' becomes 'H' (abbreviation for hospital on maps).
'rector'+'i'='rectori'
'rectori' anagrammed gives 'retoric'.
'retoric' going around 'h' is 'RHETORIC'.
'from' acts as a link.
(Other definitions for rhetoric that I've seen before include "Vague talk and empty promises" , "Effective or persuasive language" , "Eloquence" , "The art of oratory" , "The art of using words impressively" .)