New Labourite losing head, with yen to be flashy (5)
I believe the answer is:
lairy
'be flashy' is the definition.
(I've seen this before)
'new labourite losing head with yen' is the wordplay.
'new labourite' becomes 'Blair' (New Labour politician Tony Blair).
'losing head' means to remove the first letter.
'with' says to put letters next to each other.
'yen' becomes 'y' (resembles the symbol for the currency of Japan).
'blair' with its first letter taken away is 'lair'.
'lair'+'y'='LAIRY'
'to' acts as a link.
(Other definitions for lairy that I've seen before include "Flashy" , "Gave money to (someone) for work, goods, etc" , "Filthy and loud" .)