Mysterious European republic on the up (5)
I believe the answer is:
eerie
'mysterious' is the definition.
(thesaurus)
'european republic on the up' is the wordplay.
'european' becomes 'e' (abbreviation e.g. EU).
'republic' becomes 'eire' (Irish name for Ireland).
'on' says to put letters next to each other.
'the up' says the letters should be written in reverse (in down clue: letters go upwards).
'e' put after 'eire' is 'eiree'.
'eiree' back-to-front is 'EERIE'.
(Other definitions for eerie that I've seen before include "Strange, frightening" , "Uncannily strange" , "Scary, weird" , "Spooky, unearthly" , "Weird and disturbing" .)