Arabian lady’s heading off with yours truly (5)
I believe the answer is:
omani
'arabian' is the definition.
(someone from Oman)
'lady's heading off with yours truly' is the wordplay.
'lady' becomes 'woman' (I've seen this before).
'heading off' means to remove the first letter.
'with' is a charade indicator (letters next to each other).
'yours truly' becomes 'I' (the person who set this crossword).
'woman' with its initial letter removed is 'oman'.
'oman'+'i'='OMANI'
(Other definitions for omani that I've seen before include "Naomi (anag) -- from Muscat?" , "Gulf native" , "Speaker of Arabic" , "Middle East national" , "One from Muscat" .)