Investigation into popular pursuit (7)
I believe the answer is:
inquest
'investigation' is the definition.
(I know that inquest is a type of enquiry)
'popular pursuit' is the wordplay.
'popular' becomes 'in' (something that's 'in' is fashionable).
'pursuit' becomes 'quest' (synonyms).
'in'+'quest'='INQUEST'
'into' is the link.
(Other definitions for inquest that I've seen before include "Post-mortem investigation" , "Inquiry into the cause of unexpected death" , "Post-death enquiry" , "Coroner's meeting" , "Coroner's inquiry into cause of death" .)