Would he be short of a title if he lost one? (7)
I believe the answer is:
baronet
'a title if he lost one?' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'would he be short' is the wordplay.
'would he' becomes 'baron' (I am not sure about this - if you are sure you should believe this answer much more).
'be' becomes 'vet' (vetting is a kind of being).
'short' means to remove the first letter.
'vet' with its initial letter removed is 'et'.
'baron'+'et'='BARONET'
'of' is the link.
Can you help me to learn more?
(Other definitions for baronet that I've seen before include "Lower noble" , "Lowest British hereditary title" , "Hereditary knight" , "One's entitled" , "A Breton could be a British peer" .)