By shop's entrance, father catches sick on back of expensive shoe (10)
I believe the answer is:
espadrille
'shoe' is the definition.
(I know that espadrille is a type of sandal)
'by shop's entrance father catches sick on back of expensive' is the wordplay.
I cannot really see how this works, but
'father' could be 'pa' (pa can mean dad or father) and 'pa' is present in the answer.
'sick' could be 'ill' (synonyms) and 'ill' is located in the answer.
'on' could be 're' ('on' can be mean 'with reference to') and 're' is found within the leftover letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for espadrille that I've seen before include "you put your foot in it" , "Light rope-soled shoe" , "Shoe with a canvas upper" , "Cord-soled shoe" , "Plaited fibres in its sole" .)