Maiden popular with Delphi's leader is Psyche (4)
I believe the answer is:
mind
'is psyche' is the definition.
(I've seen this in another clue)
'maiden popular with delphi's leader' is the wordplay.
'maiden' becomes 'm' (cricket abbreviation).
'popular' becomes 'in' ('in' can mean trendy).
'with' means one lot of letters go next to another.
'leader' says to take the initial letters.
The initial letter of 'delphi' is 'd'.
'm'+'in'+'d'='MIND'
(Other definitions for mind that I've seen before include "Intelligence" , "Take care of; intellect" , "This can be made up" , "Take offence (at)" , "Seat of the faculty of reason" .)