The old man? Strict, bit of a nag (7)
I believe the answer is:
pastern
'bit of a nag' is the definition.
The definition and answer can be both animals as well as being singular nouns.
Perhaps there's an association between them I don't understand?
'the old man? strict' is the wordplay.
'the old man?' becomes 'pa' (both can mean father).
'strict' becomes 'stern' (I've seen this before).
'pa'+'stern'='PASTERN'
Can you help me to learn more?
(Other definitions for pastern that I've seen before include "Fetter-bone of horse" , "Wrongly-defined part of horse" , "'The knee of an horse' (Johnson)" , "Word Johnson misdefined" , "Part of horse's foot" .)