Danger of rising anger in political extremists (5)
I believe the answer is:
peril
'danger' is the definition.
(peril is a kind of danger)
'rising anger in political extremists' is the wordplay.
'rising' says the letters should be written in reverse (going up in a down clue).
'anger' becomes 'ire' (ire is intense rage).
'in' means one lot of letters goes inside another.
'extremists' suggests removing the centre.
'political' with its middle removed is 'pl'.
'ire' backwards is 'eri'.
'eri' put within 'pl' is 'PERIL'.
'of' acts as a link.
(Other definitions for peril that I've seen before include "Exposure to harm" , "Immediate danger" , "Danger of serious kind" , "Hazardous situation" , "risk" .)