Mother dear disheartened by one day in European city (6)
I believe the answer is:
madrid
'european city' is the definition.
(capital of Spain)
'mother dear disheartened by one day' is the wordplay.
'mother' becomes 'ma' (Ma is another word for mother or mum).
'disheartened' says to hollow out the word (remove centre letters) (the middle or heart is removed).
'by' says to put letters next to each other.
'one' becomes 'i' (Roman numeral).
'day' becomes 'd' (abbreviation for day).
'dear' with its centre removed is 'dr'.
'ma'+'dr'+'i'+'d'='MADRID'
'in' acts as a link.
(Other definitions for madrid that I've seen before include "Capital of Spain since 1561" , "City with the Prado national art gallery" , "Spanish city" , "Spain's capital" , "Spanish capital" .)