Investigation primarily conducted in hospital (4)
I believe the answer is:
scan
'investigation' is the definition.
(scan is a kind of investigation)
'primarily conducted in hospital' is the wordplay.
'primarily' suggests taking the first letters.
'in' means one lot of letters goes inside another.
'hospital' becomes 'san' (I've seen this in other clues).
The first letter of 'conducted' is 'c'.
'c' inserted into 'san' is 'SCAN'.
(Other definitions for scan that I've seen before include "Convert (a document) to a digital form" , "Examine (to transmit)" , "Study intently" , "Look over (in order to copy?)" , "Examine closely to analyse metrically" .)