Supervisor taking a horse with hesitation into eating-place (10)
I believe the answer is:
manageress
'supervisor' is the definition.
(I've seen this before)
'a horse with hesitation into eating-place' is the wordplay.
'horse with' becomes 'nag' (term for an old horse. I am not sure about the 'with' bit.).
'hesitation' becomes 'er' (sound used when hesitating).
'into' is an insertion indicator.
'eating place' becomes 'mess' (I've seen this before).
'a'+'nag'+'er'='anager'
'anager' inserted inside 'mess' is 'MANAGERESS'.
'taking' is the link.
(Other definitions for manageress that I've seen before include "woman to look after things" , "Supervisor" , "she'll take charge" .)