Inspiration needed as European problem returns (4)
I believe the answer is:
muse
'inspiration' is the definition.
(a muse is someone's inspiration)
'european problem returns' is the wordplay.
'european' becomes 'E' (abbreviation e.g. EU).
'problem' becomes 'sum' (arithmetic problem).
'returns' says the letters should be written backwards.
'e'+'sum'='esum'
'esum' in reverse letter order is 'MUSE'.
'needed as' is the link.
(Other definitions for muse that I've seen before include "Cogitate" , "Contemplate -- a goddess of the liberal arts" , "The source of an artist's inspiration" , "Contemplation" , "Ponder in meditative way" .)