Singular desire to be stylish (5)
I believe the answer is:
swish
'stylish' is the definition.
('swish' can be similar in meaning to 'stylish')
'singular desire' is the wordplay.
'singular' becomes 's' (abbreviation sometimes used in dictionaries).
'desire' becomes 'wish' (wishing is a kind of desiring).
's'+'wish'='SWISH'
'to be' is the link.
(Other definitions for swish that I've seen before include "Smart, fashionable" , "Classy" , "Elegant" , "Impressively smart" , "Smart; stylish" .)