Measure fabric square that king's left for European princess (9)
I believe the answer is:
stephanie
'european princess' is the definition.
(Princess Stephanie of Monaco)
'measure fabric square that king's left' is the wordplay.
'measure' becomes 'step' (step is a kind of measure).
'fabric square' becomes 'hankie' (hankerchief).
'that king' becomes 'K' (abbreviation for king in chess).
'left' is a deletion indicator (some letters have left).
'hankie' with 'k' removed is 'hanie'.
'step'+'hanie'='STEPHANIE'
'for' acts as a link.
(Other definitions for stephanie that I've seen before include "girl" , "Anti-sheep (anag) - girl's name" , "Woman" .)