An old hand at the surgery? (3)
I believe the answer is:
vet
'an old hand' is the definition.
(I've seen this in another clue)
'at the surgery?' is the wordplay.
'at' means one lot of letters go next to another.
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'surgery?' becomes 've' (I can't justify this - if you can you should give a lot more credence to this answer).
't' put after 've' is 'VET'.
Can you help me to learn more?
(Other definitions for vet that I've seen before include "animal doctor to > investigate" , "Examine carefully for suitability" , "Dog doc?" , "'Animal doctor, in short (3)'" , "Experienced" .)