It’s a hair of the dog the morning after, doctor (4)
I believe the answer is:
dram
'it's a hair' is the definition.
(thesaurus)
'morning after doctor' is the wordplay.
'morning' becomes 'am' (as in 12:00 AM).
'after' means one lot of letters go next to another.
'doctor' becomes 'Dr' (abbreviation).
'am' put after 'dr' is 'DRAM'.
'of the dog the' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for dram that I've seen before include "Wee drop of whisky?" , "Pick-me-up" , "Small drink of scotch" , "Measure of spirits" , "Tot of whisky" .)