Investigate report of European getting made public (5,3)
I believe the answer is:
check out
'investigate' is the definition.
(to check something out is to investigate it)
'report of european getting made public' is the wordplay.
'report of' indicates a 'sounds like' (homophone) clue.
'european' becomes 'czech' (Czechia is in Europe).
'getting' is a charade indicator (letters next to each other).
'made public' becomes 'out' (out can mean known to the public).
'czech' is a homophone of 'check'.
'check'+'out'='CHECK-OUT'
(Another definition for check out that I've seen is " Investigate - supermarket pay-desk".)