Vainly seek suit for Londoner (7)
I believe the answer is:
whistle
I believe this clue is a double definition.
'vainly seek' is the first definition.
(to whistle can be to wish for something in vain)
'suit for londoner' is the second definition.
('whistle [and flute]' is rhyming slang for 'suit')
(Other definitions for whistle that I've seen before include "Make cheerful sound" , "Musical with Hayley Mills" , "Pucker up and blow" , "Referee's instrument" , "He wilts (anag.)" .)