It hasn't yet been allocated, though Mullally's put her name down (10)
I believe the answer is:
unassigned
'name down' is the definition.
Both the definition and answer are adjectives. Maybe there's an association between them I don't understand?
'it hasn't yet been allocated though mullally's put her' is the wordplay.
I cannot really see how this works, but
'it' could be 'e' ('e' can mean 'electronic' which is similar to 'IT') and 'e' is located in the answer.
'put' could be 'assign' (synonyms) and 'assign' is present in the answer.
The remaining letters 'und' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for unassigned that I've seen before include "Not allocated" , "Not appointed" .)