Admit that, ultimately, the old lady must come first (5)
I believe the answer is:
grant
'admit' is the definition.
(thesaurus)
'ultimately the old lady must come first' is the wordplay.
I cannot quite understand how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is located in the answer.
'lady' could be 'gran' (I have seen 'old lady' mean 'gran' so perhaps 'lady' could also mean 'gran') and 'gran' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
'that' acts as a link.
Can you help me to learn more?
(Other definitions for grant that I've seen before include "yield" , "Give (a right); gift" , "Confer" , "Permit" , "Present" .)