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 really see 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 located in the answer.
No letters remain.
This explanation may well be incorrect...
'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" .)