Demanding old lover on island wanting man (7)
I believe the answer is:
exigent
'demanding' is the definition.
('exigent' can be similar in meaning to 'demanding')
'old lover on island wanting man' is the wordplay.
'old lover' becomes 'ex' (I've seen this in other clues).
'on' means one lot of letters go next to another.
'island' becomes 'i'.
'wanting' means one lot of letters go next to another.
'man' becomes 'gent' (I've seen this before**).
'ex'+'i'+'gent'='EXIGENT'
(Other definitions for exigent that I've seen before include "Urgent and exacting" , "Pressing; demanding" , "Demanding immediate attention" , "Exacting, requiring much" , "Pressing and urgent" .)