He makes inferences from a show of hands (7)
I believe the answer is:
palmist
'he makes inferences from a show of hands' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'he' is the wordplay.
I cannot quite understand how this works, but
'he' could be 'palm' and 'palm' is found within the answer.
The remaining letters 'ist' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for palmist that I've seen before include "Fortune reader" , "Person who tells fortunes from lines in hand" , "Hand reader" , "Fortune-teller" , "A practitioner of chiromancy" .)