Asian, one pursuing a lover around Grand Hotel (7)
I believe the answer is:
afghani
'a lover around grand hotel' is the definition.
I can't judge whether this definition defines the answer.
'asian one pursuing' is the wordplay.
'asian' becomes 'afghan' (Afghan is an example**).
'one' becomes 'i' (Roman numeral).
'pursuing' means one lot of letters go next to another.
'afghan'+'i'='AFGHANI'
(Other definitions for afghani that I've seen before include "Native of Kabul, for instance" , "Asian capital" , "Currency in Kabul" , "Asian currency" , "Native of five across" .)