Sadly an element of political asylum ... (4)
I believe the answer is:
alas
'sadly' is the definition.
('alas' is used to express regret)
'element of political asylum' is the wordplay.
'element of' says the answer is hidden in the clue (I've seen this in other clues).
'ALAS' can be found hidden inside 'political asylum'.
'an' is the link.
(Other definitions for alas that I've seen before include "Lackaday" , "Antipodean island state" , "Expression of grief or misfortune" , "express regret thus" , "Sad to say!" .)